{"id":40609,"date":"2022-04-04T13:30:24","date_gmt":"2022-04-04T08:00:24","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=40609"},"modified":"2022-04-07T11:31:37","modified_gmt":"2022-04-07T06:01:37","slug":"big-ideas-math-algebra-2-answers-chapter-5","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers-chapter-5\/","title":{"rendered":"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions"},"content":{"rendered":"<p><strong>Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions PDF<\/strong> Formatted links are enlisted here for free of cost. So, students who are looking for solutions with detailed &amp; step-wise explanations can refer to this Big Ideas math Book Algebra 2 Ch 5 Answer key and verify their answers while practicing sessions. Also, you can make use of this <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers\/\">BIM Algebra 2 Solutions<\/a> for solving homework and assignment questions of Chapter 5 Rational Exponents and Radical Functions. So, improve your math skills by accessing this ultimate guide of BigIdeasMath Algebra 2 Chapter 5 Answers Pdf.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 2 Answer Key Chapter 5 Rational Exponents and Radical Functions<\/h2>\n<p>Students can get detailed solutions for all questions included in BigIdeas Math Book Algebra 2 Chapter 5 Answer Key. The<strong> BIM Textbook Answers Algebra 2 Ch 5<\/strong> <strong>Rational Exponents and Radical Functions <\/strong>covers various preparation resources like Topic-wise exercise questions, chapter tests, reviews, practices, quiz, cumulative assessment, etc. to understand the concepts and learn efficiently. Therefore, click on the links available below and quickly access the respective exercise questions of BIM Algebra 2 Ch 5 Rational Exponents and Radical Functions for better preparation.<\/p>\n<ul>\n<li><a href=\"#Rational_Exponents_and_Radical_Functions_Maintaining_Mathematical_Proficiency\">Rational Exponents and Radical Functions Maintaining Mathematical Proficiency &#8211; Page 235<\/a><\/li>\n<li><a href=\"#Rational_Exponents_and_Radical_Functions_Mathematical_Practices\">Rational Exponents and Radical Functions Mathematical Practices &#8211; Page 236<\/a><\/li>\n<li><a href=\"#Lesson_5.1_nth_Roots_and_Rational_Exponents\">Lesson 5.1 nth Roots and Rational Exponents &#8211; Page(238-242)<\/a><\/li>\n<li><a href=\"#nth_Roots_and_Rational_Exponents_5.1_Exercises\">nth Roots and Rational Exponents 5.1 Exercises &#8211; Page(241-242)<\/a><\/li>\n<li><a href=\"#Lesson_5.2_Properties_of_Rational_Exponents_and_Radicals\">Lesson 5.2 Properties of Rational Exponents and Radicals &#8211; Page(244-250)<\/a><\/li>\n<li><a href=\"#Properties_of_Rational_Exponents_and_Radicals_5.2_Exercises\">Properties of Rational Exponents and Radicals 5.2 Exercises &#8211; Page(248-250)<\/a><\/li>\n<li><a href=\"#Lesson_5.3_Graphing_Radical_Functions\">Lesson 5.3 Graphing Radical Functions &#8211; Page(252-258)<\/a><\/li>\n<li><a href=\"#Graphing_Radical_Functions_5.3_Exercises\">Graphing Radical Functions 5.3 Exercises &#8211; Page(256-258)<\/a><\/li>\n<li><a href=\"#Rational_Exponents_and_Radical_Functions_Study_Skills\">Rational Exponents and Radical Functions Study Skills &#8211; Page 259<\/a><\/li>\n<li><a href=\"#Rational_Exponents_and_Radical_Functions_5.1_-_5.3_Quiz\">Rational Exponents and Radical Functions 5.1 &#8211; 5.3 Quiz &#8211; Page 260<\/a><\/li>\n<li><a href=\"#Lesson_5.4_Solving_Radical_Equations_and_Inequalities\">Lesson 5.4 Solving Radical Equations and Inequalities &#8211; Page(262-268)<\/a><\/li>\n<li><a href=\"#Solving_Radical_Equations_and_Inequalities_5.4_Exercises\">Solving Radical Equations and Inequalities 5.4 Exercises &#8211; Page(266-268)<\/a><\/li>\n<li><a href=\"#Lesson_5.5_Performing_Function_Operations\">Lesson 5.5 Performing Function Operations &#8211; Page(270-274)<\/a><\/li>\n<li><a href=\"#Performing_Function_Operations_5.5_Exercises\">Performing Function Operations 5.5 Exercises &#8211; Page(273-274)<\/a><\/li>\n<li><a href=\"#Lesson_5.6_Inverse_of_a_Function\">Lesson 5.6 Inverse of a Function &#8211; Page(276-284)<\/a><\/li>\n<li><a href=\"#Inverse_of_a_Function_5.6_Exercises\">Inverse of a Function 5.6 Exercises &#8211; Page(281-284)<\/a><\/li>\n<li><a href=\"#Rational_Exponents_and_Radical_Functions_Performance_Task\">Rational Exponents and Radical Functions Performance Task &#8211; Page 285<\/a><\/li>\n<li><a href=\"#Rational_Exponents_and_Radical_Functions_Chapter_Review\">Rational Exponents and Radical Functions Chapter Review &#8211; Page(286-288)<\/a><\/li>\n<li><a href=\"#Rational_Exponents_and_Radical_Functions_Chapter_Test\">Rational Exponents and Radical Functions Chapter Test &#8211; Page 289<\/a><\/li>\n<li><a href=\"#Rational_Exponents_and_Radical_Functions_Cumulative_Assessment\">Rational Exponents and Radical Functions Cumulative Assessment &#8211; Page(290-291)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Rational_Exponents_and_Radical_Functions_Maintaining_Mathematical_Proficiency\"><\/a>Rational Exponents and Radical Functions Maintaining Mathematical Proficiency<\/h3>\n<p><b>Simplify the expression<\/b><\/p>\n<p>Question 1.<br \/>\ny<sup>6<\/sup> \u2022 y<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{n^{4}}{n^{3}}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{x^{5}}{x^{6} \\cdot x^{2}}\\)<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{x^{-6}}{x^{5}}\\) \u2022 3x<sup>2\/sup&gt;<\/sup><\/p>\n<p>Question 5.<br \/>\n\\(\\left(\\frac{4 w^{3}}{2 z^{2}}\\right)^{3}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\left(\\frac{m^{7} \\cdot m}{z^{2} \\cdot m^{3}}\\right)^{2}\\)<\/p>\n<p><b>Solve the literal equation for y.<\/b><\/p>\n<p>Question 7.<br \/>\n4x + y = 2<\/p>\n<p>Question 8.<br \/>\nx \u2212 \\(\\frac{1}{3}\\)y = \u22121<\/p>\n<p>Question 9.<br \/>\n2y \u2212 9 = 13x<\/p>\n<p>Question 10.<br \/>\n2xy + 6y = 10<\/p>\n<p>Question 11.<br \/>\n8x \u2212 4xy = 3<\/p>\n<p>Question 12.<br \/>\n6x + 7xy = 15<\/p>\n<p>Question 13.<br \/>\n<b>ABSTRACT REASONING<\/b> Is the order in which you apply properties of exponents important? Explain your reasoning.<\/p>\n<h3><a id=\"Rational_Exponents_and_Radical_Functions_Mathematical_Practices\"><\/a>Rational Exponents and Radical Functions Mathematical Practices<\/h3>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 1.<br \/>\nUse the Pythagorean Theorem to find the exact lengths of a, b, c, and d in the figure.<\/p>\n<p>Question 2.<br \/>\nUse a calculator to approximate each length to the nearest tenth of an inch.<\/p>\n<p>Question 3.<br \/>\nUse a ruler to check the reasonableness of your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 1\" width=\"320\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-1.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-1-300x230.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/p>\n<h3><a id=\"Lesson_5.1_nth_Roots_and_Rational_Exponents\"><\/a>Lesson 5.1 nth Roots and Rational Exponents<\/h3>\n<p><b>Essential Question<\/b><\/p>\n<p>How can you use a rational exponent to represent a power involving a radical?<br \/>\nPreviously, you learned that the nth root of a can be represented as<br \/>\n\\(\\sqrt[n]{a}\\) = \\(a^{1 \/ n}\\) Definition of rational exponent<br \/>\nfor any real number a and integer n greater than 1.<\/p>\n<p><b>EXPLORATION 1<br \/>\nExploring the Definition of a Rational Exponent<br \/>\nWork with a partner. <\/b>Use a calculator to show that each statement is true.<br \/>\na. \\(\\sqrt{9}\\) = \\(9^{1 \/ 2}\\)<br \/>\nb. \\(\\sqrt{2}\\) = \\(2^{1 \/ 2}\\)<br \/>\nc. \\(\\sqrt[3]{8}\\) = \\(8^{1 \/ 3}\\)<br \/>\nd. \\(\\sqrt[3]{3}\\) = \\(3^{1 \/ 3}\\)<br \/>\ne. \\(\\sqrt[4]{16}\\) = \\(16^{1 \/ 4}\\)<br \/>\nf. \\(\\sqrt[4]{12}\\) = \\(12^{1 \/ 4}\\)<\/p>\n<p><b>EXPLORATION 2<br \/>\nWriting Expressions in Rational Exponent Form<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 2\" width=\"226\" height=\"188\" \/><br \/>\n<b>Work with a partner. <\/b>Use the definition of a rational exponent and the properties of exponents to write each expression as a base with a single rational exponent. Then use a calculator to evaluate each expression. Round your answer to two decimal places.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40656\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 3\" width=\"382\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-3.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-3-300x99.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><br \/>\na. \\((\\sqrt{5})^{3}\\)<br \/>\nb. \\((\\sqrt[4]{4})^{2}\\)<br \/>\nc. \\((\\sqrt[3]{9})^{2}\\)<br \/>\nd. \\((\\sqrt[5]{10})^{4}\\)<br \/>\ne. \\((\\sqrt{15})^{3}\\)<br \/>\nf. \\((\\sqrt[3]{27})^{4}\\)<\/p>\n<p><b>EXPLORATION 3<br \/>\nWriting Expressions in Radical Form<br \/>\nWork with a partner.<\/b> Use the properties of exponents and the definition of a rational exponent to write each expression as a radical raised to an exponent. Then use a calculator to evaluate each expression. Round your answer to two decimal places.<br \/>\nSample \\(5^{2 \/ 3}\\) = (\\left(5^{1 \/ 3}\\right)\\(\\))<sup>2<\/sup> = (\\((\\sqrt[3]{5})\\))<sup>2<\/sup> \u2248 2.92<br \/>\na. \\(8^{2 \/ 3}\\)<br \/>\nb. \\(6^{5 \/ 2}\\)<br \/>\nc. \\(12^{3 \/ 4}\\)<br \/>\nd. \\(10^{3 \/ 2}\\)<br \/>\ne. \\(16^{3 \/ 2}\\)<br \/>\nf. \\(20^{6 \/ 5}\\)<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 4.<br \/>\nHow can you use a rational exponent to represent a power involving a radical?<\/p>\n<p>Question 5.<br \/>\nEvaluate each expression without using a calculator. Explain your reasoning.<br \/>\na. \\(4^{3 \/ 2}\\)<br \/>\nb. \\(32^{4 \/ 5}\\)<br \/>\nc. \\(625^{3 \/ 4}\\)<br \/>\nd. \\(49^{3 \/ 2}\\)<br \/>\ne. \\(125^{4 \/ 3}\\)<br \/>\nf. \\(100^{6 \/ 3}\\)<\/p>\n<p><b>5.1 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 1.<br \/>\nn = 4, a = 16<\/p>\n<p>Question 2.<br \/>\nn = 2, a = \u221249<\/p>\n<p>Question 3.<br \/>\nn = 3, a = \u2212125<\/p>\n<p>Question 4.<br \/>\nn = 5, a = 243<\/p>\n<p><b>Evaluate the expression without using a calculator.<\/b><\/p>\n<p>Question 5.<br \/>\n\\(4^{5 \/ 2}\\)<\/p>\n<p>Question 6.<br \/>\n\\(9^{-1 \/ 2}\\)<\/p>\n<p>Question 7.<br \/>\n\\(81^{3 \/ 4}\\)<\/p>\n<p>Question 8.<br \/>\n\\(1^{7 \/ 8}\\)<\/p>\n<p><b>Evaluate the expression using a calculator. Round your answer to two decimal places when appropriate.<\/b><\/p>\n<p>Question 9.<br \/>\n\\(6^{2 \/ 5}\\)<\/p>\n<p>Question 10.<br \/>\n\\(64^{-2 \/ 3}\\)<\/p>\n<p>Question 11.<br \/>\n\\((\\sqrt[4]{16})^{5}\\)<\/p>\n<p>Question 12.<br \/>\n\\((\\sqrt[3]{-30})^{2}\\)<\/p>\n<p><b>Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate.<\/b><\/p>\n<p>Question 13.<br \/>\n8x<sup>3<\/sup> = 64<\/p>\n<p>Question 14.<br \/>\n\\([\\frac{1}{2}\/latex]x<sup>5<\/sup> = 512<\/p>\n<p>Question 15.<br \/>\n(x + 5)<sup>4<\/sup> = 16<\/p>\n<p>Question 16.<br \/>\n(x \u2212 2)<sup>3<\/sup> = \u221214<\/p>\n<p>Question 17.<br \/>\n<b>WHAT IF? <\/b>In Example 5, what is the annual depreciation rate when the salvage value is $6000?<\/p>\n<h3><a id=\"nth_Roots_and_Rational_Exponents_5.1_Exercises\"><\/a>nth Roots and Rational Exponents 5.1 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>VOCABULARY<\/b> Rewrite the expression [latex]a^{-s \/ t}\\) in radical form. Then state the index of the radical.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46559\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 1\" width=\"530\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-1.png 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-1-300x36.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>COMPLETE THE SENTENCE<\/b> For an integer n greater than 1, if b<sup>n<\/sup> = a, then bis a(n) ___________ of a.<br \/>\n<span style=\"font-size: 16px;\">Answer:<\/span><\/p>\n<p>Question 3.<br \/>\n<b>WRITING<\/b> Explain how to use the sign of a to determine the number of real fourth roots of a and the number of real fifth roots of a.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 3\" width=\"579\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-3.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-3-300x58.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>WHICH ONE DOESN\u2019T BELONG? <\/b>Which expression does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40657\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 4\" width=\"565\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-4.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-4-300x27.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 5\u201310, find the indicated real nth root(s) of a.<\/b><\/p>\n<p>Question 5.<br \/>\nn = 3, a = 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46561\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 5\" width=\"565\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-5.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-5-300x31.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 6.<br \/>\nn = 5, a = \u22121<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nn = 2, a = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46562\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 7\" width=\"555\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-7.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-7-300x32.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 8.<br \/>\nn = 4, a = 256<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nn = 5, a = \u221232<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 9\" width=\"495\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-9.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-9-300x52.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 10.<br \/>\nn = 6, a = \u2212729<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 11\u201318, evaluate the expression without using a calculator.<\/b><\/p>\n<p>Question 11.<br \/>\n\\(64^{1 \/ 6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 11\" width=\"179\" height=\"36\" \/><\/p>\n<p>Question 12.<br \/>\n\\(8^{1 \/ 3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n\\(25^{3 \/ 2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46565\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 13\" width=\"255\" height=\"34\" \/><\/p>\n<p>Question 14.<br \/>\n\\(81^{3 \/ 4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n\\((-243)^{1 \/ 5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46566\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 15\" width=\"289\" height=\"34\" \/><\/p>\n<p>Question 16.<br \/>\n\\((-64)^{4 \/ 3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(8^{-2 \/ 3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46567\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 17\" width=\"301\" height=\"58\" \/><\/p>\n<p>Question 18.<br \/>\n\\(16^{-7 \/ 4}\\)<br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 19 and 20, describe and correct the error in evaluating the expression.<\/b><\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5\" width=\"321\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5-300x96.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46568\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 19\" width=\"392\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-19.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-19-300x103.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 6\" width=\"315\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-6.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-6-300x103.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\nAnswer:<\/p>\n<p><b>USING STRUCTURE In Exercises 21\u201324, match the equivalent expressions. Explain your reasoning.<\/b><\/p>\n<p>Question 21.<br \/>\n\\((\\sqrt[3]{5})^{4}\\) A. \\(5^{-1 \/ 4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46569\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 21\" width=\"574\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-21.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-21-300x30.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 22.<br \/>\n\\((\\sqrt[4]{5})^{3}\\) B. \\(5^{4 \/ 3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n\\(\\frac{1}{\\sqrt[4]{5}}\\) C. \\(-5^{1 \/ 4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46570\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 23\" width=\"556\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-23.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-23-300x32.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 24.<br \/>\n\\(-\\sqrt[4]{5}\\) D. \\(5^{3 \/ 4}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 25\u201332, evaluate the expression using a calculator. Round your answer to two decimal places when appropriate.<\/b><\/p>\n<p>Question 25.<br \/>\n\\(\\sqrt[5]{32,768}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 25\" width=\"140\" height=\"40\" \/><\/p>\n<p>Question 26.<br \/>\n\\(\\sqrt[7]{1695}\\)<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n\\(25^{-1 \/ 3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46572\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 27\" width=\"134\" height=\"30\" \/><\/p>\n<p>Question 28.<br \/>\n\\(85^{1 \/ 6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n\\(20,736^{4 \/ 5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46573\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 29\" width=\"195\" height=\"34\" \/><\/p>\n<p>Question 30.<br \/>\n\\(86^{-5 \/ 6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n\\((\\sqrt[4]{187})^{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46574\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 31\" width=\"168\" height=\"45\" \/><\/p>\n<p>Question 32.<br \/>\n\\((\\sqrt[5]{-8})^{8}\\)<br \/>\nAnswer:<\/p>\n<p><b>MATHEMATICAL CONNECTIONS In Exercises 33 and 34, find the radius of the figure with the given volume.<\/b><\/p>\n<p>Question 33.<br \/>\nV = 216 ft<sup>3<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40660\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 7\" width=\"133\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46575\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 33\" width=\"563\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-33.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-33-300x129.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 34.<br \/>\nV = 1332 cm<sup>3<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-8.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 8\" width=\"164\" height=\"125\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 35\u201344, find the real solution(s) of the equation. Round your answer to two decimal places when appropriate.<\/b><\/p>\n<p>Question 35.<br \/>\nx<sup>3<\/sup> = 125<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46576\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 35\" width=\"216\" height=\"98\" \/><\/p>\n<p>Question 36.<br \/>\n5x<sup>3<\/sup> = 1080<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n(x + 10)<sup>5<\/sup> = 70<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46577\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 37\" width=\"200\" height=\"162\" \/><\/p>\n<p>Question 38.<br \/>\n(x \u2212 5)<sup>4<\/sup> = 256<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nx<sup>5<\/sup> = \u221248<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46578\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 39\" width=\"247\" height=\"99\" \/><\/p>\n<p>Question 40.<br \/>\n7x<sup>4<\/sup> = 56<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nx<sup>6<\/sup> + 36 = 100<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46579\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 41\" width=\"196\" height=\"162\" \/><\/p>\n<p>Question 42.<br \/>\nx<sup>3<\/sup> + 40 = 25<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n\\(\\frac{1}{3}\\)x<sup>4<\/sup> = 27<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46580\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 43\" width=\"341\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-43.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-43-300x125.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<p>Question 44.<br \/>\n\\(\\frac{1}{6}\\)x<sup>3<\/sup> = \u221236<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>When the average price of an item increases from p<sub>1<\/sub> to p<sub>2<\/sub> over a period of n years, the annual rate of inflation r (in decimal form) is given by r = \\(\\left(\\frac{p_{2}}{p_{1}}\\right)^{1 \/ n}\\) \u2212 1. Find the rate of inflation for each item in the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 9\" width=\"258\" height=\"154\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46581\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-45.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 45.1\" width=\"551\" height=\"425\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-45.1.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-45.1-300x231.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46582\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-45.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 45.2\" width=\"509\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-45.2.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-45.2-300x116.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> The graph of y = x<sup>n<\/sup> is shown in red. What can you conclude about the value of n? Determine the number of real nth roots of a. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-10.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 10\" width=\"212\" height=\"179\" \/><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<b>NUMBER SENSE<\/b> Between which two consecutive integers does \\(\\sqrt[4]{125}\\) lie? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46583\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 47\" width=\"526\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-47.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-47-300x36.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>THOUGHT PROVOKING<\/b> In 1619, Johannes Kepler published his third law, which can be given by d<sup>3<\/sup> = t<sup>2<\/sup>, where d is the mean distance (in astronomical units) of a planet from the Sun and t is the time (in years) it takes the planet to orbit the Sun. It takes Mars 1.88 years to orbit the Sun. Graph a possible location of Mars. Justify your answer. (The diagram shows the Sun at the origin of the xy-plane and a possible location of Earth.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40664\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 11\" width=\"292\" height=\"138\" \/><br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<b>PROBLEM SOLVING<\/b> A weir is a dam that is built across a river to regulate the flow of water. The flow rate Q (in cubic feet per second) can be calculated using the formula Q= 3.367\u2113\\(h^{3 \/ 2}\\), where \u2113 is the length (in feet) of the bottom of the spillway and his the depth (in feet) of the water on the spillway. Determine the flow rate of a weir with a spillway that is 20 feet long and has a water depth of 5 feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40665\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-12.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 12\" width=\"265\" height=\"145\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46584\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 49\" width=\"549\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-49.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-49-300x63.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>REPEATED REASONING<\/b> The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain river normally flows at a speed of 1 meter per second. What must its speed be in order to transport particles that are twice as massive as usual? 10 times as massive? 100 times as massive?<br \/>\nAnswer:<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Simplify the expression. Write your answer using only positive exponents. <\/b>(Skills Review Handbook)<\/p>\n<p>Question 51.<br \/>\n5 \u2022 5<sup>4<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46585\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 51\" width=\"187\" height=\"28\" \/><\/p>\n<p>Question 52.<br \/>\n\\(\\frac{4^{2}}{4^{7}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n\\(\\left(z^{2}\\right)^{-3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46586\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 53\" width=\"242\" height=\"60\" \/><\/p>\n<p>Question 54.<br \/>\n\\(\\left(\\frac{3 x}{2}\\right)^{4}\\)<br \/>\nAnswer:<\/p>\n<p><b>Write the number in standard form. <\/b>(Skills Review Handbook)<\/p>\n<p>Question 55.<br \/>\n5 \u00d7 10<sup>3<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46587\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 55\" width=\"160\" height=\"32\" \/><\/p>\n<p>Question 56.<br \/>\n4 \u00d7 10<sup>\u22122<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n8.2 \u00d7 10<sup>\u22121<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46588\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.1-Question-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.1 Question 57\" width=\"179\" height=\"31\" \/><\/p>\n<p>Question 58.<br \/>\n6.93 \u00d7 10<sup>6<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.2_Properties_of_Rational_Exponents_and_Radicals\"><\/a>Lesson 5.2 Properties of Rational Exponents and Radicals<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you use properties of exponents to simplify products and quotients of radicals?<\/p>\n<p><b>EXPLORATION 1<br \/>\nReviewing Properties of Exponents<br \/>\nWork with a partner.<\/b> Let a and b be real numbers. Use the properties of exponents to complete each statement. Then match each completed statement with the property it illustrates.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40666\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 13\" width=\"569\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-13.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-13-300x150.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nSimplifying Expressions with Rational Exponents<br \/>\nWork with a partner. <\/b>Show that you can apply the properties of integer exponents to rational exponents by simplifying each expression. Use a calculator to check your answers.<br \/>\na. \\(5^{2 \/ 3}\\) \u2022 \\(5^{4 \/ 3}\\)<br \/>\nb. \\(3^{1 \/ 5}\\) \u2022 \\(3^{4 \/ 5}\\)<br \/>\nc. \\(\\left(4^{2 \/ 3}\\right)^{3}\\)<br \/>\nd. \\(\\frac{\\sqrt{98}}{\\sqrt{2}}\\)<br \/>\ne. \\(\\frac{\\sqrt[4]{4}}{\\sqrt[4]{1024}}\\)<br \/>\nf. \\(\\frac{\\sqrt[3]{625}}{\\sqrt[3]{5}}\\)<\/p>\n<p><b>EXPLORATION 3<br \/>\nSimplifying Products and Quotients of Radicals<br \/>\nWork with a partner.<\/b> Use the properties of exponents to write each expression as a single radical. Then evaluate each expression. Use a calculator to check your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40667\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-14.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 14\" width=\"249\" height=\"387\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-14.png 249w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-14-193x300.png 193w\" sizes=\"(max-width: 249px) 100vw, 249px\" \/><br \/>\na. \\(\\sqrt{3}\\) \u2022 \\(\\sqrt{12}\\)<br \/>\nb. \\(\\sqrt[3]{5}\\) \u2022 \\(\\sqrt[3]{25}\\)<br \/>\nc. \\(\\sqrt[4]{27}\\) \u2022 \\(\\sqrt[4]{3}\\)<br \/>\nd. \\(\\frac{\\sqrt{98}}{\\sqrt{2}}\\)<br \/>\ne. \\(\\frac{\\sqrt[4]{4}}{\\sqrt[4]{1024}}\\)<br \/>\nf. \\(\\frac{\\sqrt[3]{625}}{\\sqrt[3]{5}}\\)<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 4.<br \/>\nHow can you use properties of exponents to simplify products and quotients of radicals?<\/p>\n<p>Question 5.<br \/>\nSimplify each expression.<br \/>\na. \\(\\sqrt{27}\\) \u2022 \\(\\sqrt{6}\\)<br \/>\nb. \\(\\frac{\\sqrt[3]{240}}{\\sqrt[3]{15}}\\)<br \/>\nc. (\\(5^{1 \/ 2}\\) \\(16^{1 \/ 4}\\))<sup>2<\/sup><\/p>\n<p><b>5.2 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Simplify the expression.<\/b><\/p>\n<p>Question 1.<br \/>\n\\(2^{3 \/ 4}\\) \u2022 \\(2^{1 \/ 2}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{3}{3^{1 \/ 4}}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\left(\\frac{20^{1 \/ 2}}{5^{1 \/ 2}}\\right)^{3}\\)<\/p>\n<p>Question 4.<br \/>\n(\\(5^{1 \/ 3}\\) \u2022 \\(7^{1 \/ 4}\\))<sup>3<\/sup><\/p>\n<p><b>Simplify the expression<\/b><\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt[4]{27}\\) \u2022 \\(\\sqrt[4]{3}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{\\sqrt[3]{250}}{\\sqrt[3]{2}}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt[3]{104}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt[5]{\\frac{3}{4}}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{3}{6-\\sqrt{2}}\\)<\/p>\n<p>Question 10.<br \/>\n\\(7 \\sqrt[5]{12}\\) &#8211; \\(\\sqrt[5]{12}\\)<\/p>\n<p>Question 11.<br \/>\n4(\\(9^{2 \/ 3}\\)) + (\\(9^{2 \/ 3}\\))<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt[3]{5}\\) + \\(\\sqrt[3]{40}\\)<\/p>\n<p><b>Simplify the expression. Assume all variables are positive.<\/b><\/p>\n<p>Question 13.<br \/>\n\\(\\sqrt[3]{27 q^{9}}\\)<\/p>\n<p>Question 14.<br \/>\n\\(\\sqrt[5]{\\frac{x^{10}}{y^{5}}}\\)<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{6 x y^{3 \/ 4}}{3 x^{1 \/ 2} y^{1 \/ 2}}\\)<\/p>\n<p>Question 16.<br \/>\n\\(\\sqrt{9} w^{5}\\) &#8211; \\(w \\sqrt{w^{3}}\\)<\/p>\n<h3><a id=\"Properties_of_Rational_Exponents_and_Radicals_5.2_Exercises\"><\/a>Properties of Rational Exponents and Radicals 5.2 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING <\/b>How do you know when a radical expression is in simplest form?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46589\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 1\" width=\"557\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-1.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-1-300x59.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WHICH ONE DOESN\u2019T BELONG?<\/b> Which radical expression does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 15\" width=\"629\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-15.png 629w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-15-300x32.png 300w\" sizes=\"(max-width: 629px) 100vw, 629px\" \/><br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u201312, use the properties of rational exponents to simplify the expression.<\/b><\/p>\n<p>Question 3.<br \/>\n\\(\\left(9^{2}\\right)^{1 \/ 3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46590\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 3\" width=\"119\" height=\"29\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\left(12^{2}\\right)^{1 \/ 4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{6}{6^{1 \/ 4}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46591\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 5\" width=\"194\" height=\"54\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{7}{7^{1 \/ 3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\left(\\frac{8^{4}}{10^{4}}\\right)^{-1 \/ 4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46592\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 7\" width=\"234\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-7.png 234w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-7-150x150.png 150w\" sizes=\"(max-width: 234px) 100vw, 234px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\left(\\frac{9^{3}}{6^{3}}\\right)^{-1 \/ 3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n(\\(3^{-2 \/ 3}\\) \u2022 \\(3^{1 \/ 3}\\))<sup>-1<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46593\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 9\" width=\"332\" height=\"272\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-9.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-9-300x246.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><\/p>\n<p>Question 10.<br \/>\n(\\(5^{1 \/ 2}\\) \u2022 \\(5^{-3 \/ 2}\\))<sup>-1\/4<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{2^{2 \/ 3} \\cdot 16^{2 \/ 3}}{4^{2 \/ 3}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46594\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 11\" width=\"359\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-11.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-11-300x85.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p>Question 12.<br \/>\n\\(\\frac{49^{3 \/ 8} \\cdot 49^{7 \/ 8}}{7^{5 \/ 4}}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 13\u201320, use the properties of radicals to simplify the expression.<\/b><\/p>\n<p>Question 13.<br \/>\n\\(\\sqrt{2}\\) \u2022 \\(\\sqrt{72}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46595\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 13\" width=\"216\" height=\"105\" \/><\/p>\n<p>Question 14.<br \/>\n\\(\\sqrt[3]{16}\\) \u2022 \\(\\sqrt[3]{32}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n\\(\\sqrt[4]{6}\\) \u2022 \\(\\sqrt[4]{8}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 15\" width=\"216\" height=\"139\" \/><\/p>\n<p>Question 16.<br \/>\n\\(\\sqrt[4]{8}\\) \u2022 \\(\\sqrt[4]{8}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{\\sqrt[5]{486}}{\\sqrt[5]{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 17\" width=\"284\" height=\"77\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\frac{\\sqrt{2}}{\\sqrt{32}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{\\sqrt[3]{6} \\cdot \\sqrt[3]{72}}{\\sqrt[3]{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46598\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 19\" width=\"354\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-19.png 354w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-19-300x63.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\frac{\\sqrt[3]{3} \\cdot \\sqrt[3]{18}}{\\sqrt[6]{2} \\cdot \\sqrt[6]{2}}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 21\u201328, write the expression in simplest form.<\/b><\/p>\n<p>Question 21.<br \/>\n\\(\\sqrt[4]{567}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46599\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 21\" width=\"195\" height=\"100\" \/><\/p>\n<p>Question 22.<br \/>\n\\(\\sqrt[5]{288}\\)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n\\(\\frac{\\sqrt[3]{5}}{\\sqrt[3]{4}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46600\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 23\" width=\"187\" height=\"208\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\frac{\\sqrt[4]{4}}{\\sqrt[4]{27}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n\\(\\sqrt{\\frac{3}{8}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46601\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 25\" width=\"190\" height=\"208\" \/><\/p>\n<p>Question 26.<br \/>\n\\(\\sqrt[3]{\\frac{7}{4}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n\\(\\sqrt[3]{\\frac{64}{49}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46602\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 27\" width=\"222\" height=\"213\" \/><\/p>\n<p>Question 28.<br \/>\n\\(\\sqrt[4]{\\frac{1296}{25}}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 29\u201336, write the expression in simplest form.<\/b><\/p>\n<p>Question 29.<br \/>\n\\(\\frac{1}{1+\\sqrt{3}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46603\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 29\" width=\"292\" height=\"259\" \/><\/p>\n<p>Question 30.<br \/>\n\\(\\frac{1}{2+\\sqrt{5}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n\\(\\frac{5}{3-\\sqrt{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46604\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 31\" width=\"305\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-31.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-31-300x265.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 32.<br \/>\n\\(\\frac{11}{9-\\sqrt{6}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n\\(\\frac{9}{\\sqrt{3}+\\sqrt{7}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 33\" width=\"347\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-33.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-33-300x231.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Question 34.<br \/>\n\\(\\frac{2}{\\sqrt{8}+\\sqrt{7}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n\\(\\frac{\\sqrt{6}}{\\sqrt{3}-\\sqrt{5}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46606\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 35\" width=\"347\" height=\"328\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-35.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-35-300x284.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Question 36.<br \/>\n\\(\\frac{\\sqrt{7}}{\\sqrt{10}-\\sqrt{2}}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 37\u201346, simplify the expression.<\/b><\/p>\n<p>Question 37.<br \/>\n\\(9 \\sqrt[3]{11}\\) + \\(3 \\sqrt[3]{11}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46607\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 37\" width=\"300\" height=\"77\" \/><\/p>\n<p>Question 38.<br \/>\n\\(8 \\sqrt[6]{5}\\) &#8211; \\(12 \\sqrt[6]{5}\\)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n\\(3\\left(11^{1 \/ 4}\\right)\\) + \\(9\\left(11^{1 \/ 4}\\right)\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 39\" width=\"336\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-39.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-39-300x59.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p>Question 40.<br \/>\n\\(13\\left(8^{3 \/ 4}\\right)\\) &#8211; \\(4\\left(8^{3 \/ 4}\\right)\\)<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n\\(5 \\sqrt{12}\\) &#8211; \\(19 \\sqrt{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46609\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 41\" width=\"346\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-41.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-41-300x153.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/p>\n<p>Question 42.<br \/>\n\\(27 \\sqrt{6}\\) + \\(7 \\sqrt{150}\\)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n\\(\\sqrt[5]{224}\\) + \\(3 \\sqrt[5]{7}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46610\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 43\" width=\"350\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-43.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-43-300x150.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/p>\n<p>Question 44.<br \/>\n\\(7 \\sqrt[3]{2}\\) &#8211; \\(\\sqrt[3]{128}\\)<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n\\(5\\left(24^{1 \/ 3}\\right)\\) &#8211; 4(\\(\\left(3^{1 \/ 3}\\right)\\))<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46611\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 45\" width=\"398\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-45.png 398w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-45-300x130.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p>\n<p>Question 46.<br \/>\n\\(5^{1 \/ 4}\\) + 6(\\([405^{1 \/ 4}\/latex])<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<b>ERROR ANALYSIS <\/b>Describe and correct the error in simplifying the expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-16.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 16\" width=\"360\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-16.png 360w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-16-300x157.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 47\" width=\"514\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-47.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-47-300x55.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>MULTIPLE REPRESENTATIONS<\/b> Which radical expressions are like radicals?<br \/>\nA. [latex]\\left(5^{2 \/ 9}\\right)^{3 \/ 2}\\)<br \/>\nB. \\(\\frac{5^{3}}{(\\sqrt[3]{5})^{8}}\\)<br \/>\nC. \\(\\sqrt[3]{625}\\)<br \/>\nD. \\(\\sqrt[3]{5} 145\\) &#8211; \\(\\sqrt[3]{875}\\)<br \/>\nE. \\(\\sqrt[3]{5}\\) + \\(3 \\sqrt[3]{5}\\)<br \/>\nF. \\(7 \\sqrt[4]{80}\\) &#8211; \\(2 \\sqrt[4]{405}\\)<br \/>\n<span style=\"font-size: 16px;\">Answer:<\/span><\/p>\n<p><b>In Exercises 49\u201354, simplify the expression.<\/b><\/p>\n<p>Question 49.<br \/>\n\\(\\sqrt[4]{81 y^{8}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46613\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 49\" width=\"234\" height=\"109\" \/><\/p>\n<p>Question 50.<br \/>\n\\(\\sqrt[3]{64 r^{3} t^{6}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n\\(\\sqrt[5]{\\frac{m^{10}}{n^{5}}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46614\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 51\" width=\"189\" height=\"189\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-51.png 189w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-51-150x150.png 150w\" sizes=\"(max-width: 189px) 100vw, 189px\" \/><\/p>\n<p>Question 52.<br \/>\n\\(\\sqrt[4]{\\frac{k^{16}}{16 z^{4}}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n\\(\\sqrt[6]{\\frac{g^{6} h}{h^{7}}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46615\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 53\" width=\"200\" height=\"252\" \/><\/p>\n<p>Question 54.<br \/>\n\\(\\sqrt[8]{n^{2} p^{-1}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<b>ERROR ANALYSIS<\/b> Describe and correct the error in simplifying the expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 17\" width=\"312\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-17.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-17-300x213.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46616\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 55\" width=\"591\" height=\"331\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-55.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-55-300x168.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 56.<br \/>\n<b>OPEN-ENDED<\/b> Write two variable expressions involving radicals, one that needs absolute value in simplifying and one that does not need absolute value. Justify your answers.<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 57\u201364, write the expression in simplest form. Assume all variables are positive.<\/b><\/p>\n<p>Question 57.<br \/>\n\\(\\sqrt{81 a^{7} b^{12} c^{9}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46617\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 57\" width=\"347\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-57.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-57-300x90.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Question 58.<br \/>\n\\(\\sqrt[3]{125 r^{4} s^{9} t^{7}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n\\(\\sqrt[5]{\\frac{160 m^{6}}{n^{7}}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46618\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-59.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 59\" width=\"290\" height=\"447\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-59.png 290w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-59-195x300.png 195w\" sizes=\"(max-width: 290px) 100vw, 290px\" \/><\/p>\n<p>Question 60.<br \/>\n\\(\\sqrt[4]{\\frac{405 x^{3} y^{3}}{5 x^{-1} y}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n\\(\\frac{\\sqrt[3]{w} \\cdot \\sqrt{w^{5}}}{\\sqrt{25 w^{16}}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46619\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-61.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 61\" width=\"256\" height=\"298\" \/><\/p>\n<p>Question 62.<br \/>\n\\(\\frac{\\sqrt[4]{v^{6}}}{\\sqrt[7]{v^{5}}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n\\(\\frac{18 w^{1 \/ 3} v^{5 \/ 4}}{27 w^{4 \/ 3} v^{1 \/ 2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46620\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-63.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 63\" width=\"296\" height=\"221\" \/><\/p>\n<p>Question 64.<br \/>\n\\(\\frac{7 x^{-3 \/ 4} y^{5 \/ 2} z^{-2 \/ 3}}{56 x^{-1 \/ 2} y^{1 \/ 4}}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 65\u201370, perform the indicated operation. Assume all variables are positive.<\/b><\/p>\n<p>Question 65.<br \/>\n\\(12 \\sqrt[3]{y}\\) + \\(9 \\sqrt[3]{y}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46621\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-65.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 65\" width=\"281\" height=\"71\" \/><\/p>\n<p>Question 66.<br \/>\n\\(11 \\sqrt{2 z}\\) &#8211; \\(5 \\sqrt{2 z}\\)<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n\\(3 x^{7 \/ 2}\\) &#8211; 5\\(x^{7 \/ 2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46622\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-67.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 67\" width=\"246\" height=\"64\" \/><\/p>\n<p>Question 68.<br \/>\n\\(7 \\sqrt[3]{m^{7}}\\) + \\(3 m^{7 \/ 3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n\\(\\sqrt[4]{16 w^{10}}\\) + \\(2 w \\sqrt[4]{w^{6}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-69.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 69\" width=\"425\" height=\"224\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-69.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-69-300x158.png 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>Question 70.<br \/>\n(p<sup>1\/2<\/sup> \u2022 p<sup>1\/4<\/sup>) &#8211; \\(\\sqrt[4]{16 p^{3}}\\)<br \/>\nAnswer:<\/p>\n<p><b>MATHEMATICAL CONNECTIONS In Exercises 71 and 72, find simplified expressions for the perimeter and area of the given figure.<\/b><\/p>\n<p>Question 71.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-18.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 18\" width=\"147\" height=\"98\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46624\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-71.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 71\" width=\"383\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-71.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-71-300x75.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n<p>Question 72<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40672\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 19\" width=\"165\" height=\"118\" \/><br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>The optimum diameter d (in millimeters) of the pinhole in a pinhole camera can be modeled by d = 1.9[(5.5 \u00d7 10<sup>\u22124<\/sup>)\u2113]<sup>1\/2<\/sup>, where \u2113 is the length (in millimeters) of the camera box. Find the optimum pinhole diameter for a camera box with a length of 10 centimeters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-20.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 20\" width=\"353\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-20.png 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-20-300x121.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46625\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-73.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 73\" width=\"553\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-73.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-73-300x107.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 74.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> The surface area S(in square centimeters) of a mammal can be modeled by S = km<sup>2\/3<\/sup>, where m is the mass (in grams) of the mammal and k is a constant. The table shows the values of k for different mammals.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 21\" width=\"302\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-21.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-21-300x85.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\na. Find the surface area of a bat whose mass is 32 grams.<br \/>\nb. Find the surface area of a rabbit whose mass is 3.4 kilograms (3.4 \u00d7 10<sup>3<\/sup> grams).<br \/>\nc. Find the surface area of a human whose mass is 59 kilograms.<br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\n<b>MAKING AN ARGUMENT<\/b> Your friend claims it is not possible to simplify the expression 7\\(\\sqrt{11}\\) \u2212 9 \\(\\sqrt{44}\\) because it does not contain like radicals. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46626\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-75.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 75\" width=\"586\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-75.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-75-300x118.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 76.<br \/>\n<b>PROBLEM SOLVING <\/b>The apparent magnitude of a star is a number that indicates how faint the star is in relation to other stars. The expression f(x) = \\(\\frac{2.512^{m_{1}}}{2.512^{m_{2}}}\\) tells how many times fainter a star with apparent magnitude m<sub>1<\/sub> is than a star with apparent magnitude m<sub>2<\/sub>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-22.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 22\" width=\"360\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-22.png 360w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-22-300x131.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><br \/>\na. How many times fainter is Altair than Vega?<br \/>\nb. How many times fainter is Deneb than Altair?<br \/>\nc. How many times fainter is Deneb than Vega?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 23\" width=\"282\" height=\"190\" \/><br \/>\nAnswer:<\/p>\n<p>Question 77.<br \/>\n<b>CRITICAL THINKING<\/b> Find a radical expression for the perimeter of the triangle inscribed in the square shown. Simplify the expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40677\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-24.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 24\" width=\"136\" height=\"138\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-77.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 77\" width=\"564\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-77.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-77-300x131.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 78.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>Without finding points, match the functions f(x) = \\(\\sqrt{64 x^{2}}\\) and g(x) = \\(\\sqrt[3]{64 x^{6}}\\) with their graphs. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 25\" width=\"399\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-25.png 399w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-25-300x151.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 79.<br \/>\n<b>REWRITING A FORMULA <\/b>You have filled two round balloons with water. One balloon contains twice as much water as the other balloon.<br \/>\na. Solve the formula for the volume of a sphere, V = \\(\\frac{4}{3}\\)\u03c0r<sup>3<\/sup>, for r.<br \/>\nb. Substitute the expression for r from part (a) into the formula for the surface area of a sphere, S = 4\u03c0r<sup>2<\/sup>. Simplify to show that S = (4\u03c0)<sup>1\/3<\/sup>(3V)<sup>2\/3<\/sup>.<br \/>\nc. Compare the surface areas of the two water balloons using the formula in part (b).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46628\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-79.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 79.1\" width=\"295\" height=\"600\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-79.1.png 295w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-79.1-148x300.png 148w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46629\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-79.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 79.2\" width=\"567\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-79.2.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-79.2-300x90.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 80.<br \/>\n<b>THOUGHT PROVOKING <\/b>Determine whether the expressions (x<sup>2<\/sup>)<sup>1\/6<\/sup> and (x<sup>1\/6<\/sup>)<sup>2<\/sup> are equivalent for all values of x.<br \/>\nAnswer:<\/p>\n<p>Question 81.<br \/>\n<b>DRAWING CONCLUSIONS <\/b>Substitute different combinations of odd and even positive integers for m and n in the expression \\(\\sqrt[n]{x^{m}}\\). When you cannot assume x is positive, explain when absolute value is needed in simplifying the expression.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46630\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-81.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 81\" width=\"551\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-81.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-81-300x35.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><br \/>\n<b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Identify the focus, directrix, and axis of symmetry of the parabola. Then graph the equation. <\/b>(Section 2.3)<\/p>\n<p>Question 82.<br \/>\ny = 2x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 83.<br \/>\ny<sup>2<\/sup> = \u2212x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46631\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-83.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 83.1\" width=\"572\" height=\"492\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-83.1.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-83.1-300x258.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46632\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-83.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 83.2\" width=\"341\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-83.2.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-83.2-300x215.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<p>Question 84.<br \/>\ny<sup>2<\/sup> = 4x<br \/>\nAnswer:<\/p>\n<p><b>Write a rule for g. Describe the graph of g as a transformation of the graph of f. <\/b>(Section 4.7)<\/p>\n<p>Question 85.<br \/>\nf(x) = x<sup>4<\/sup> \u2212 3x<sup>2<\/sup> \u2212 2x, g(x) = \u2212f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46633\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-85.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 85\" width=\"389\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-85.png 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-85-300x126.png 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 86.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 x, g(x) = f(x) \u2212 3<br \/>\nAnswer:<\/p>\n<p>Question 87.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 4, g(x) = f(x \u2212 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-87.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.2 Question 87\" width=\"548\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-87.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.2-Question-87-300x57.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 88.<br \/>\nf(x) = x<sup>4<\/sup> + 2x<sup>3<\/sup> \u2212 4x<sup>2<\/sup>, g(x) = f(2x)<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.3_Graphing_Radical_Functions\"><\/a>Lesson 5.3 Graphing Radical Functions<\/h3>\n<p><b>Essential Question<\/b><\/p>\n<p>How can you identify the domain and range of a radical function?<\/p>\n<p><b>EXPLORATION 1<br \/>\nIdentifying Graphs of Radical Functions<br \/>\nWork with a partner.<\/b> Match each function with its graph. Explain your reasoning. Then identify the domain and range of each function.<br \/>\na. f(x) = \\(\\sqrt{x}\\)<br \/>\nb. f(x) = \\(\\sqrt[3]{x}\\)<br \/>\nc. f(x) = \\(\\sqrt[4]{x}\\)<br \/>\nd. f(x) = \\(\\sqrt[5]{x}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-26.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 26\" width=\"520\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-26.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-26-300x177.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nIdentifying Graphs of Transformations<br \/>\nWork with a partner. <\/b>Match each transformation of f(x) = \\(\\sqrt{x}\\) with its graph. Explain your reasoning. Then identify the domain and range of each function.<br \/>\na. g(x) = \\(\\sqrt{x+2}\\)<br \/>\nb. g(x) = \\(\\sqrt{x-2}\\)<br \/>\nc. g(x) = \\(\\sqrt{x}+2-2\\)<br \/>\nd. g(x) = \u2212\\(\\sqrt{x+2}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40680\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 27\" width=\"522\" height=\"309\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-27.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-27-300x178.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you identify the domain and range of a radical function?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40682\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-28.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 28\" width=\"252\" height=\"181\" \/><br \/>\nQuestion 4.<br \/>\nUse the results of Exploration 1 to describe how the domain and range of a radical function are related to the index of the radical.<\/p>\n<p><b>5.3 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 1.<br \/>\nGraph g(x) = \\(\\sqrt{x+1}\\). Identify the domain and range of the function.<\/p>\n<p>Question 2.<br \/>\nDescribe the transformation of f(x) = \\(\\sqrt[3]{x}\\) represented by g(x) = \u2212\\(\\sqrt[3]{x}\\) \u2212 2. Then graph each function.<\/p>\n<p>Question 3.<br \/>\n<b>WHAT IF? <\/b>In Example 3, the function N(d ) = 2.4 \u2022 E(d) approximates the number of seconds it takes a dropped object to fall d feet on the Moon. Write a rule for N. How long does it take a dropped object to fall 25 feet on the Moon?<\/p>\n<p>Question 4.<br \/>\nIn Example 4, is the transformed function the same when you perform the translation followed by the horizontal shrink? Explain your reasoning.<\/p>\n<p>Question 5.<br \/>\nUse a graphing calculator to graph \u22124y<sup>2<\/sup> = x + 1. Identify the vertex and the direction that the parabola opens.<\/p>\n<p>Question 6.<br \/>\nUse a graphing calculator to graph x<sup>2<\/sup> + y<sup>2<\/sup> = 25. Identify the radius and the intercepts.<\/p>\n<h3><a id=\"Graphing_Radical_Functions_5.3_Exercises\"><\/a>Graphing Radical Functions 5.3 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b> Square root functions and cube root functions are examples of __________ functions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46635\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 1\" width=\"581\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-1.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-1-300x28.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>COMPLETE THE SENTENCE<\/b> When graphing y = a\\(\\sqrt[3]{x-h}\\) + k, translate the graph of y = a\\(\\sqrt[3]{x}\\)h units __________ and k units __________.<br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u20138, match the function with its graph.<\/b><\/p>\n<p>Question 3.<br \/>\nf(x) = \\(\\sqrt{x}+3\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46636\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 3\" width=\"582\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-3.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-3-300x30.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 4.<br \/>\nh(x) = \\(\\sqrt{x}\\) + 3<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nf(x) = \\(\\sqrt{x-3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46637\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 5\" width=\"563\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-5.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-5-300x44.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 6.<br \/>\ng(x) = \\(\\sqrt{x}\\) \u2212 3<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nh(x) = \\(\\sqrt{x+3}\\) \u2212 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46638\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 7\" width=\"580\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-7.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-7-300x44.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 8.<br \/>\nf(x) = \\(\\sqrt{x-3}\\) + 3<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40681\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-28.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 28.1\" width=\"389\" height=\"411\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-28.1.png 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-28.1-284x300.png 284w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p><b>In Exercises 9\u201318, graph the function. Identify the domain and range of the function.<\/b><\/p>\n<p>Question 9.<br \/>\nh(x) = \\(\\sqrt{x}\\) + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46639\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 9\" width=\"560\" height=\"529\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-9.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-9-300x283.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 10.<br \/>\ng(x) = \\(\\sqrt{x}\\) \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ng(x) = \u2212 \\(\\sqrt[3]{2 x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46640\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 11\" width=\"554\" height=\"401\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-11.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-11-300x217.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 12.<br \/>\nf(x) = \\(\\sqrt[3]{-5 x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\ng(x) = \\(\\frac{1}{5} \\sqrt{x}-3\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46641\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 13\" width=\"548\" height=\"383\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-13.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-13-300x210.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 14.<br \/>\nf(x) = \\(\\frac{1}{2} \\sqrt[3]{x}+6\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nf(x) = \\((6 x)^{1 \/ 2}\\) + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46642\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 15\" width=\"552\" height=\"555\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-15.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-15-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-15-150x150.png 150w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 16.<br \/>\ng(x) = \u22123(x + 1)<sup>1\/3<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nh(x) = \u2212\\(\\sqrt[4]{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46643\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 17\" width=\"543\" height=\"385\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-17.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-17-300x213.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 18.<br \/>\nh(x) = \\(\\sqrt[5]{2 x}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 19\u201326, describe the transformation of f represented by g. Then graph each function.<\/b><\/p>\n<p>Question 19.<br \/>\nf(x) = \\(\\sqrt{x}\\), g(x) = \\(\\sqrt{x+1}\\) + 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 19\" width=\"566\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-19.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-19-300x250.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 20.<br \/>\nf(x) = \\(\\sqrt{x}\\), g(x) = 2\\(\\sqrt{x-1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nf(x) = \\(\\sqrt[3]{x}\\), g(x) = \u2212\\(\\sqrt[3]{x}\\) \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46645\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 21\" width=\"561\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-21.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-21-300x129.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 22.<br \/>\nf(x) = \\(\\sqrt[3]{x}\\), g(x) = \\(\\sqrt[3]{x+4}\\) \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nf(x) = \\(x^{1 \/ 2}\\), g(x) = \\(\\frac{1}{4}(-x)^{1 \/ 2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 23\" width=\"574\" height=\"264\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-23.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-23-300x138.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 24.<br \/>\nf(x) = \\(x^{1 \/ 3}\\), g(x) = \\(\\frac{1}{3} x^{1 \/ 3}\\) + 6<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nf(x) = \\(\\sqrt[4]{x}\\), g(x) = \\(2 \\sqrt[4]{x+5}\\) \u2212 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46647\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 25\" width=\"550\" height=\"350\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-25.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-25-300x191.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 26.<br \/>\nf(x) = \\(\\sqrt[5]{x}\\), g(x) = \\(\\sqrt[5]{-32 x}\\) + 3<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<b>ERROR ANALYSIS<\/b> Describe and correct the error in graphing f(x) = \\(\\sqrt{x-2}\\) \u2212 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40683\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 29\" width=\"256\" height=\"173\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 27\" width=\"564\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-27.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-27-300x108.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 28.<br \/>\n<b>ERROR ANALYSIS<\/b> Describe and correct the error in describing the transformation of the parent square root function represented by g(x) = \\(\\sqrt{\\frac{1}{2} x}\\) + 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-30.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 30\" width=\"378\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-30.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-30-300x94.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><br \/>\nAnswer:<\/p>\n<p><b>USING TOOLS In Exercises 29\u201334, use a graphing calculator to graph the function. Then identify the domain and range of the function.<\/b><\/p>\n<p>Question 29.<br \/>\ng(x) = \\(\\sqrt{x^{2}+x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 29\" width=\"278\" height=\"232\" \/><\/p>\n<p>Question 30.<br \/>\nh(x) = \\(\\sqrt{x^{2}-2 x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nf(x) = \\(\\sqrt[3]{x^{2}+x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 31\" width=\"578\" height=\"436\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-31.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-31-300x226.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 32.<br \/>\nf(x) = \\(\\sqrt[3]{3 x^{2}-x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nf(x) = \\(\\sqrt{2 x^{2}+x+1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 33\" width=\"574\" height=\"443\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-33.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-33-300x232.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 34.<br \/>\nh(x) = \\(\\sqrt[3]{\\frac{1}{2} x^{2}-3 x+4}\\)<br \/>\nAnswer:<\/p>\n<p><b>ABSTRACT REASONING In Exercises 35\u201338, complete the statement with sometimes, always, or never.<\/b><\/p>\n<p>Question 35.<br \/>\nThe domain of the function y = a\\(\\sqrt{x}\\) is ______ x \u2265 0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 35\" width=\"495\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-35.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-35-300x22.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 36.<br \/>\nThe range of the function y = a\\(\\sqrt{x}\\) is ______ y \u2265 0.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\nThe domain and range of the function y = \\(\\sqrt[3]{x-h}\\) + k are ________ all real numbers.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 37\" width=\"548\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-37.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-37-300x36.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 38.<br \/>\nThe domain of the function y = a\\(\\sqrt{-x}\\) + k is ________ x \u2265 0.<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<b>PROBLEM SOLVING <\/b>The distance (in miles) a pilot can see to the horizon can be approximated by E(n) = 1.22\\(\\sqrt{n}\\), where n is the plane\u2019s altitude (in feet above sea level) on Earth. The function M(n) = 0.75E(n) approximates the distance a pilot can see to the horizon n feet above the surface of Mars. Write a rule for M. What is the distance a pilot can see to the horizon from an altitude of 10,000 feet above Mars?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40685\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 31\" width=\"351\" height=\"148\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-31.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-31-300x126.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 39\" width=\"557\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-39.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-39-300x110.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 40.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> The speed (in knots) of sound waves in air can be modeled by<br \/>\nv(K) = 643.855\\(\\sqrt{\\frac{K}{273.15}}\\)<br \/>\nwhere K is the air temperature (in kelvin). The speed (in meters per second) of sound waves in air can be modeled by s(K) = \\(\\frac{v(K)}{1.944}\\)<br \/>\nWrite a rule for s. What is the speed (in meters per second) of sound waves when the air temperature is 305 kelvin?<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 41\u201344, write a rule for g described by the transformations of the graph of f.<\/b><\/p>\n<p>Question 41.<br \/>\nLet g be a vertical stretch by a factor of 2, followed by a translation 2 units up of the graph of f(x) = \\(\\sqrt{x}\\) + 3.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 41\" width=\"583\" height=\"362\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-41.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-41-300x186.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 42.<br \/>\nLet g be a reflection in the y-axis, followed by a translation 1 unit right of the graph of f(x) = \\(2 \\sqrt[3]{x-1}\\).<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nLet g be a horizontal shrink by a factor of \\(\\frac{2}{3}\\), followed by a translation 4 units left of the graph of f(x) = \\(\\sqrt{6 x}\\).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46657\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 43\" width=\"590\" height=\"383\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-43.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-43-300x195.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 44.<br \/>\nLet g be a translation 1 unit down and 5 units right, followed by a reflection in the x-axis of the graph of f(x) = \u2212\\(-\\frac{1}{2} \\sqrt[4]{x}+\\frac{3}{2}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 45 and 46, write a rule for g.<\/b><\/p>\n<p>Question 45.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40686\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-32.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 32\" width=\"156\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 45\" width=\"575\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-45.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-45-300x173.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 46.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 33\" width=\"154\" height=\"148\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 47\u201350, write a rule for g that represents the indicated transformation of the graph of f.<\/b><\/p>\n<p>Question 47.<br \/>\nf(x) = 2\\(\\sqrt{x}\\), g(x) = f(x + 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 47\" width=\"549\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-47.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-47-300x61.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 48.<br \/>\nf(x) = \\(\\frac{1}{3} \\sqrt{x-1}\\), g(x) = \u2212f(x) + 9<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\nf(x) = \u2212\\(\\sqrt{x^{2}-2}\\), g(x) = \u22122f(x + 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46660\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 49\" width=\"586\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-49.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-49-300x133.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 50.<br \/>\nf(x) = \\(\\sqrt[3]{x^{2}+10 x}\\), g(x) =\\(\\frac{1}{4}\\)f(\u2212x) + 6<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 51\u201356, use a graphing calculator to graph the equation of the parabola. Identify the vertex and the direction that the parabola opens.<\/b><\/p>\n<p>Question 51.<br \/>\n\\(\\frac{1}{4}\\)y<sup>2<\/sup> = x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 51\" width=\"524\" height=\"333\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-51.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-51-300x191.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p>Question 52.<br \/>\n3y<sup>2<\/sup> = x<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n\u22128y<sup>2<\/sup> + 2 = x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 53\" width=\"560\" height=\"412\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-53.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-53-300x221.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 54.<br \/>\n2y<sup>2<\/sup> = x \u2212 4<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\nx + 8 = \\(\\frac{1}{5}\\)y<sup>2<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 55\" width=\"554\" height=\"341\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-55.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-55-300x185.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 56.<br \/>\n\\(\\frac{1}{2}\\)x = y<sup>2<\/sup> \u2212 4<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 57\u201362, use a graphing calculator to graph the equation of the circle. Identify the radius and the intercepts.<\/b><\/p>\n<p>Question 57.<br \/>\nx<sup>2<\/sup> + y<sup>2<\/sup> = 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46664\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 57\" width=\"558\" height=\"369\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-57.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-57-300x198.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 58.<br \/>\nx<sup>2<\/sup> + y<sup>2<\/sup> = 4<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n1 \u2212 y<sup>2<\/sup> = x<sup>2<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46665\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-59.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 59\" width=\"539\" height=\"364\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-59.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-59-300x203.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 60.<br \/>\n64 \u2212 x<sup>2<\/sup> = y<sup>2<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n\u2212y<sup>2<\/sup> = x<sup>2<\/sup> \u2212 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46666\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-61.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 61\" width=\"585\" height=\"392\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-61.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-61-300x201.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 62.<br \/>\nx<sup>2<\/sup> = 100 \u2212 y<sup>2<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>The period of a pendulum is the time the pendulum takes to complete one back-and-forth swing. The period T (in seconds) can be modeled by the function T = 1.11\\(\\sqrt{\\ell}\\), where \u2113 is the length (in feet) of the pendulum. Graph the function. Estimate the length of a pendulum with a period of 2 seconds. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40688\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-34.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 34\" width=\"212\" height=\"204\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46667\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-63.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 63\" width=\"545\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-63.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-63-300x144.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 64.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> Does the graph represent a square root function or a cube root function? Explain. What are the domain and range of the function?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40689\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 35\" width=\"162\" height=\"137\" \/><br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<b>PROBLEM SOLVING<\/b> For a drag race car with a total weight of 3500 pounds, the speed s(in miles per hour) at the end of a race can be modeled by s = 14.8\\(\\sqrt[3]{p}\\), where p is the power (in horsepower). Graph the function.<br \/>\na. Determine the power of a 3500-pound car that reaches a speed of 200 miles per hour.<br \/>\nb. What is the average rate of change in speed as the power changes from 1000 horsepower to 1500 horsepower?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-65.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 65\" width=\"578\" height=\"434\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-65.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-65-300x225.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 66.<br \/>\n<b>THOUGHT PROVOKING<\/b> The graph of a radical function f passes through the points (3, 1) and (4, 0). Write two different functions that could represent f(x + 2) + 1. Explain.<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n<b>MULTIPLE REPRESENTATIONS<\/b> The terminal velocity v<sub>t<\/sub>(in feet per second) of a skydiver who weighs 140 pounds is given by v<sub>t<\/sub> = 33.7\\(\\sqrt{\\frac{140}{\\Lambda}}\\)<br \/>\nwhere A is the cross-sectional surface area (in square feet) of the skydiver. The table shows the terminal velocities (in feet per second) for various surface areas (in square feet) of a skydiver who weighs 165 pounds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-36.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 36\" width=\"284\" height=\"178\" \/><br \/>\na. Which skydiver has a greater terminal velocity for each value of A given in the table?<br \/>\nb. Describe how the different values of A given in the table relate to the possible positions of the falling skydiver.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-67.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 67\" width=\"592\" height=\"294\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-67.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-67-300x149.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 68.<br \/>\n<b>MATHEMATICAL CONNECTIONS <\/b>The surface area S of a right circular cone with a slant height of 1 unit is given by S = \u03c0r + \u03c0r<sup>2<\/sup>, where r is the radius of the cone.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 37\" width=\"152\" height=\"130\" \/><br \/>\na. Use completing the square to show that r = \\(\\frac{1}{\\sqrt{\\pi}} \\sqrt{S+\\frac{\\pi}{4}}-\\frac{1}{2}\\).<br \/>\nb. Graph the equation in part (a) using a graphing calculator. Then find the radius of a right circular cone with a slant height of 1 unit and a surface area of \\(\\frac{3 \\pi}{4}\\) square units.<br \/>\nAnswer:<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Solve the equation. Check your solutions. <\/b>(Skills Review Handbook)<\/p>\n<p>Question 69.<br \/>\n| 3x + 2 | = 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-69.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 69\" width=\"381\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-69.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-69-300x143.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/p>\n<p>Question 70.<br \/>\n\u22234x + 9 \u2223 = \u22127<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n| 2x \u2212 6 \u2223 = \u2223 x \u2223<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-71.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 71\" width=\"362\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-71.png 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-71-300x145.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><\/p>\n<p>Question 72.<br \/>\n| x + 8 | = | 2x + 2 |<br \/>\nAnswer:<\/p>\n<p><b>Solve the inequality. <\/b>(Section 3.6)<\/p>\n<p>Question 73.<br \/>\nx<sup>2<\/sup> + 7x + 12 &lt; 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46672\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-73.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 73\" width=\"573\" height=\"570\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-73.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-73-300x298.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-73-150x150.png 150w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 74.<br \/>\nx<sup>2<\/sup> \u2212 10x + 25 \u2265 4<br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\n2x<sup>2<\/sup> + 6 &gt; 13x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-75.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.3 Question 75\" width=\"606\" height=\"641\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-75.png 606w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.3-Question-75-284x300.png 284w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<p>Question 76.<br \/>\n\\(\\frac{1}{8}\\)x<sup>2<\/sup> + x \u2264 \u22122<br \/>\nAnswer:<\/p>\n<h3><a id=\"Rational_Exponents_and_Radical_Functions_Study_Skills\"><\/a>Rational Exponents and Radical Functions Study Skills : Analyzing Your Errors<\/h3>\n<p><b>5.1\u20135.3 What Did You Learn?<\/b><\/p>\n<p><b>Core Vocabulary<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-38.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 38\" width=\"553\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-38.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-38-300x43.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p><b>Core Concepts<\/b><br \/>\n<b>Section 5.1<\/b><br \/>\nReal nth Roots of a, p. 238<br \/>\nRational Exponents, p. 239<\/p>\n<p><b>Section 5.2<\/b><br \/>\nProperties of Rational Exponents, p. 244<br \/>\nProperties of Radicals, p. 245<\/p>\n<p><b>Section 5.3<\/b><br \/>\nParent Functions for Square Root and Cube Root Functions, p. 252<br \/>\nTransformations of Radical Functions, p. 253<\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nHow can you use definitions to explain your reasoning in Exercises 21\u201324 on page 241?<\/p>\n<p>Question 2.<br \/>\nHow did you use structure to solve Exercise 76 on page 250?<\/p>\n<p>Question 3.<br \/>\nHow can you check that your answer is reasonable in Exercise 39 on page 257?<\/p>\n<p>Question 4.<br \/>\nHow can you make sense of the terms of the surface area formula given in Exercise 68 on page 258?<\/p>\n<p><b>Study Skills<\/b><br \/>\n<b>Analyzing Your Errors<\/b><br \/>\n<b>Application Errors<\/b><br \/>\n<b>What Happens:<\/b> You can do numerical problems, but you struggle with problems that have context.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40693\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 39\" width=\"443\" height=\"310\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-39.png 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-39-300x210.png 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><br \/>\n<b>How to Avoid This Error: <\/b>Do not just mimic the steps of solving an application problem. Explain out loud what the question is asking and why you are doing each step. After solving the problem, ask yourself, \u201cDoes my solution make sense?\u201d<\/p>\n<h3><a id=\"Rational_Exponents_and_Radical_Functions_5.1_-_5.3_Quiz\"><\/a>Rational Exponents and Radical Functions 5.1 &#8211; 5.3 Quiz<\/h3>\n<p><b>5.1\u20135.3 Quiz<\/b><\/p>\n<p><b>Find the indicated real nth root(s) of a. <\/b>(Section 5.1)<\/p>\n<p>Question 1.<br \/>\nn = 4, a = 81<\/p>\n<p>Question 2.<br \/>\nn = 5, a = \u22121024<\/p>\n<p>Question 3.<br \/>\nEvaluate (a) 16<sup>3\/4<\/sup> and (b) 125<sup>2\/3<\/sup> without using a calculator. Explain your reasoning. (Section 5.1)<\/p>\n<p><b>Find the real solution(s) of the equation. Round your answer to two decimal places.<\/b>(Section 5.1)<\/p>\n<p>Question 4.<br \/>\n2x<sup>6<\/sup> = 1458<\/p>\n<p>Question 5.<br \/>\n(x + 6)<sup>3<\/sup> = 28<\/p>\n<p><b>Simplify the expression.<\/b>(Section 5.2)<\/p>\n<p>Question 6.<br \/>\n\\(\\left(\\frac{48^{1 \/ 4}}{6^{1 \/ 4}}\\right)^{6}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt[4]{3}\\) \u2022 \\(\\sqrt[4]{432}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{1}{3+\\sqrt{2}}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt[3]{16}\\) &#8211; \\(5 \\sqrt[3]{2}\\)<\/p>\n<p>Question 10.<br \/>\nSimplify \\(\\sqrt[8]{x^{9} y^{8} z^{16}}\\). (Section 5.2)<\/p>\n<p><b>Write the expression in simplest form. Assume all variables are positive<\/b>.(Section 5.2)<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt[3]{216 p^{9}}\\)<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{\\sqrt[5]{32}}{\\sqrt[5]{m^{3}}}\\)<\/p>\n<p>Question 13.<br \/>\n\\(\\sqrt[4]{n^{4} q}\\) + \\(7 n \\sqrt[4]{q}\\)<\/p>\n<p>Question 14.<br \/>\nGraph f(x) = 2\\(2 \\sqrt[3]{x}\\) + 1. Identify the domain and range of the function. (Section 5.3)<\/p>\n<p><b>Describe the transformation of the parent function represented by the graph of g. Then write a rule for g.<\/b>(Section 5.3)<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40694\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-40.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 40\" width=\"188\" height=\"176\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40695\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 41\" width=\"186\" height=\"181\" \/><\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40696\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-42.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 42\" width=\"179\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-42.png 179w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-42-150x150.png 150w\" sizes=\"(max-width: 179px) 100vw, 179px\" \/><\/p>\n<p>Question 18.<br \/>\nUse a graphing calculator to graph x = 3y<sup>2<\/sup> \u2212 6. Identify the vertex and direction the parabola opens. (Section 5.3)<\/p>\n<p>Question 19.<br \/>\nA jeweler is setting a stone cut in the shape of a regular octahedron. A regular octahedron is a solid with eight equilateral triangles as faces, as shown. The formula for the volume of the stone is V= 0.47s<sup>3<\/sup>, where s is the side length (in millimeters) of an edge of the stone. The volume of the stone is 161 cubic millimeters. Find the length of an edge of the stone. (Section 5.1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 43\" width=\"109\" height=\"105\" \/><\/p>\n<p>Question 20.<br \/>\nAn investigator can determine how fast a car was traveling just prior to an accident using the model s = 4\\(\\sqrt{d}\\), where s is the speed (in miles per hour) of the car and d is the length (in feet) of the skid marks. Graph the model. The length of the skid marks of a car is 90 feet. Was the car traveling at the posted speed limit prior to the accident? Explain your reasoning. (Section 5.3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40698\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-44.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 44\" width=\"113\" height=\"157\" \/><\/p>\n<h3><a id=\"Lesson_5.4_Solving_Radical_Equations_and_Inequalities\"><\/a>Lesson 5.4 Solving Radical Equations and Inequalities<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you solve a radical equation?<\/p>\n<p><b>EXPLORATION 1<br \/>\nSolving Radical Equations<br \/>\nWork with a partner. <\/b>Match each radical equation with the graph of its related radical function. Explain your reasoning. Then use the graph to solve the equation, if possible. Check your solutions.<br \/>\na. \\(\\sqrt{x-1}\\) &#8211; 1 = 0<br \/>\nb. \\(\\sqrt{2 x+2}\\) &#8211; \\(\\sqrt{x+4}\\) = 0<br \/>\nc. \\(\\sqrt{9-x^{2}}\\) = 0<br \/>\nd. \\(\\sqrt{x+2}\\) &#8211; x = 0<br \/>\ne. \\(\\sqrt{-x+2}\\) &#8211; x = 0<br \/>\nf. \\(\\sqrt{3 x^{2}+1}\\) = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 45\" width=\"542\" height=\"452\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-45.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-45-300x250.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nSolving Radical Equations<br \/>\nWork with a partner.<\/b> Look back at the radical equations in Exploration 1. Suppose that you did not know how to solve the equations using a graphical approach.<br \/>\na. Show how you could use a numerical approach to solve one of the equations. For instance, you might use a spreadsheet to create a table of values.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-46.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 46\" width=\"259\" height=\"180\" \/><br \/>\nb. Show how you could use an analytical approach to solve one of the equations. For instance, look at the similarities between the equations in Exploration 1. What first step may be necessary so you could square each side to eliminate the radical(s)? How would you proceed to find the solution?<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you solve a radical equation?<\/p>\n<p>Question 4.<br \/>\nWould you prefer to use a graphical, numerical, or analytical approach to solve the given equation? Explain your reasoning. Then solve the equation.<br \/>\n\\(\\sqrt{x+3}\\) &#8211; \\(\\sqrt{x-2}\\) = 1<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the equation. Check your solution.<\/b><\/p>\n<p>Question 1.<br \/>\n\\(\\sqrt[3]{x}\\) &#8211; 9 = -6<\/p>\n<p>Question 2.<br \/>\n\\(\\sqrt{x+25}\\) = 2<\/p>\n<p>Question 3.<br \/>\n2\\(\\sqrt[3]{x-3}\\) = 4<\/p>\n<p>Question 4.<br \/>\n<b>WHAT IF? <\/b>Estimate the air pressure at the center of the hurricane when the mean sustained wind velocity is 48.3 meters per second.<\/p>\n<p><b>Solve the equation. Check your solution(s).<\/b><\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt{10 x+9}\\) = x + 3<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt{2 x+5}\\) = \\(\\sqrt{x+7}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt{x+6}\\) &#8211; 2 = \\(\\sqrt{x-2}\\)<\/p>\n<p><b>Solve the equation. Check your solution(s).<\/b><\/p>\n<p>Question 8.<br \/>\n(3x)<sup>1\/3<\/sup> = \u22123<\/p>\n<p>Question 9.<br \/>\n(x + 6)<sup>1\/2<\/sup> = x<\/p>\n<p>Question 10.<br \/>\n(x + 2)<sup>3\/4<\/sup> = 8<\/p>\n<p>Question 11.<br \/>\nSolve<br \/>\n(a) 2\\(\\sqrt{x}\\) \u2212 3 \u2265 3 and<br \/>\n(b) 4\\(\\sqrt[3]{x+1}\\) &lt; 8<\/p>\n<h3><a id=\"Solving_Radical_Equations_and_Inequalities_5.4_Exercises\"><\/a>Solving Radical Equations and Inequalities 5.4 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>VOCABULARY<\/b> Is the equation 3x \u2212 \\(\\sqrt{2}\\) = \\(\\sqrt{6}\\) a radical equation? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 1\" width=\"547\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-1.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-1-300x32.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WRITING<\/b> Explain the steps you should use to solve \\(\\sqrt{x}\\) + 10 &lt; 15<br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u201312, solve the equation. Check your solution.<\/b><\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt{5 x+1}\\) = 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 3\" width=\"528\" height=\"194\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-3.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-3-300x110.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt{3 x+10}\\) = 8<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt[3]{x-16}\\) = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 5\" width=\"511\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-5.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-5-300x92.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt[3]{x}\\) \u2212 10 = \u22127<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\u22122\\(\\sqrt{24 x}\\) + 13 = \u22121<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46677\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 7\" width=\"517\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-7.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-7-300x155.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/p>\n<p>Question 8.<br \/>\n8\\(\\sqrt[3]{10 x}\\) \u2212 15 = 17<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{1}{5} \\sqrt[3]{3 x}\\) = 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 9\" width=\"583\" height=\"252\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-9.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-9-300x130.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt{2 x}-\\frac{2}{3}\\) = 0<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(2 \\sqrt[5]{x}\\) + 7 = 15<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 11\" width=\"541\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-11.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-11-300x105.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt[4]{4 x}\\) \u2212 13 = \u221215<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> Biologists have discovered that the shoulder height h (in centimeters) of a male Asian elephant can be modeled by h = 62.5\\(\\sqrt[3]{t}\\) + 75.8, where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 250 centimeters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40701\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 47\" width=\"316\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-47.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-47-300x207.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46680\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 13\" width=\"587\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-13.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-13-300x140.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 14.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> In an amusement park ride, a rider suspended by cables swings back and forth from a tower. The maximum speed v (in meters per second) of the rider can be approximated by v = \\(\\sqrt{2 g h}\\), where h is the height (in meters) at the top of each swing and g is the acceleration due to gravity (g \u2248 9.8 m\/sec<sup>2<\/sup>). Determine the height at the top of the swing of a rider whose maximum speed is 15 meters per second.<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 15\u201326, solve the equation. Check your solution(s).<\/b><\/p>\n<p>Question 15.<br \/>\nx\u2212 6 = \\(\\sqrt{3 x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46681\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 15\" width=\"432\" height=\"436\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-15.png 432w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-15-297x300.png 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-15-150x150.png 150w\" sizes=\"(max-width: 432px) 100vw, 432px\" \/><\/p>\n<p>Question 16.<br \/>\nx \u2212 10 = \\(\\sqrt{9 x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(\\sqrt{44-2 x}\\) = x \u2212 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46683\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 17\" width=\"376\" height=\"570\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-17.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-17-198x300.png 198w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\sqrt{2 x+30}\\) = x + 3<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\\(\\sqrt[3]{8 x^{3}-1}\\) = 2x \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 19\" width=\"534\" height=\"450\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-19.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-19-300x253.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\sqrt[4]{3-8 x^{2}}\\) = 2x<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n\\(\\sqrt{4 x+1}\\) = \\(\\sqrt{x+10}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46685\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 21\" width=\"546\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-21.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-21-300x95.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 22.<br \/>\n\\(\\sqrt{3 x-3}\\) &#8211; \\(\\sqrt{x+12}\\) = 0<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n\\(\\sqrt[3]{2 x-5}\\) &#8211; \\(\\sqrt[3]{8 x+1}\\) = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46686\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 23\" width=\"429\" height=\"373\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-23.png 429w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-23-300x261.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\sqrt[3]{x+5}\\) = 2\\(\\sqrt[3]{2 x+6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n\\(\\sqrt{3 x-8}\\) + 1 = \\(\\sqrt{x+5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-25.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 25.1\" width=\"514\" height=\"458\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-25.1.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-25.1-300x267.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46688\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-25.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 25.2\" width=\"392\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-25.2.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-25.2-300x284.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Question 26.<br \/>\n\\(\\sqrt{x+2}\\) = 2 &#8211; \\(\\sqrt{x}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 27\u201334, solve the equation. Check your solution(s).<\/b><\/p>\n<p>Question 27.<br \/>\n2x<sup>2\/3<\/sup> = 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46689\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 27\" width=\"517\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-27.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-27-300x109.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/p>\n<p>Question 28.<br \/>\n4x<sup>3\/2<\/sup> = 32<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nx<sup>1\/4<\/sup> + 3 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 29\" width=\"559\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-29.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-29-300x82.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 30.<br \/>\n2x<sup>3\/4<\/sup> \u2212 14 = 40<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n(x + 6)<sup>1\/2<\/sup> = x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 31\" width=\"461\" height=\"425\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-31.png 461w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-31-300x277.png 300w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/p>\n<p>Question 32.<br \/>\n(5 \u2212 x)<sup>1\/2<\/sup> \u2212 2x = 0<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n2(x + 11)<sup>1\/2<\/sup> = x + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-33.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 33.1\" width=\"548\" height=\"498\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-33.1.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-33.1-300x273.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 34.<br \/>\n(5x<sup>2<\/sup> \u2212 4)<sup>1\/4<\/sup> = x<br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 35 and 36, describe and correct the error in solving the equation.<\/b><\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40702\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-48.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 48\" width=\"266\" height=\"144\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46693\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-35.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 35.1\" width=\"256\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-35.1.png 256w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-35.1-150x150.png 150w\" sizes=\"(max-width: 256px) 100vw, 256px\" \/><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 49\" width=\"285\" height=\"135\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 37\u201344, solve the inequality.<\/b><\/p>\n<p>Question 37.<br \/>\n\\(2 \\sqrt[3]{x}\\) \u2212 5 \u2265 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46694\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 37\" width=\"231\" height=\"210\" \/><\/p>\n<p>Question 38.<br \/>\n\\(\\sqrt[3]{x-4}\\) \u2264 5<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n\\(4 \\sqrt{x-2}\\) &gt; 20<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46695\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 39\" width=\"248\" height=\"308\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-39.png 248w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-39-242x300.png 242w\" sizes=\"(max-width: 248px) 100vw, 248px\" \/><\/p>\n<p>Question 40.<br \/>\n7\\(\\sqrt{x}\\) + 1 &lt; 9<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n2\\(\\sqrt{x}\\) + 3 \u2264 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46696\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 41\" width=\"273\" height=\"278\" \/><\/p>\n<p>Question 42.<br \/>\n\\(\\sqrt[3]{x+7}\\) \u2265 3<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n\\(-2 \\sqrt[3]{x+4}\\) &lt; 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 43\" width=\"251\" height=\"209\" \/><\/p>\n<p>Question 44.<br \/>\n\u22120.25\\(\\sqrt{x}\\) \u2212 6 \u2264 \u22123<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>The length \u2113 (in inches) of a standard nail can be modeled by \u2113 = 54d<sup>3\/2<\/sup>, where d is the diameter (in inches) of the nail. What is the diameter of a standard nail that is 3 inches long?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46698\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 45\" width=\"558\" height=\"229\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-45.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-45-300x123.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>DRAWING CONCLUSIONS<\/b> \u201cHang time\u201d is the time you are suspended in the air during a jump. Your hang time t (in seconds) is given by the function t = 0.5\\(\\sqrt{h}\\), where h is the height (in feet) of the jump. Suppose a kangaroo and a snowboarder jump with the hang times shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-50.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 50\" width=\"359\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-50.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-50-300x150.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><br \/>\na. Find the heights that the snowboarder and the kangaroo jump.<br \/>\nb. Double the hang times of the snowboarder and the kangaroo and calculate the corresponding heights of each jump.<br \/>\nc. When the hang time doubles, does the height of the jump double? Explain.<br \/>\nAnswer:<\/p>\n<p><b>USING TOOLS In Exercises 47\u201352, solve the nonlinear system. Justify your answer with a graph.<\/b><\/p>\n<p>Question 47.<br \/>\ny<sup>2<\/sup> = x \u2212 3<br \/>\ny = x \u2212 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 47\" width=\"562\" height=\"579\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-47.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-47-291x300.png 291w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 48.<br \/>\ny<sup>2<\/sup> = 4x + 17<br \/>\ny = x + 5<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\nx<sup>2<\/sup> + y<sup>2<\/sup> = 4<br \/>\ny = x &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 49\" width=\"565\" height=\"640\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-49.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-49-265x300.png 265w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 50.<br \/>\nx<sup>2<\/sup> + y<sup>2<\/sup> = 25<br \/>\ny = \\(-\\frac{3}{4}\\)x + \\(\\frac{25}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\nx<sup>2<\/sup> + y<sup>2<\/sup> = 1<br \/>\ny = \\(\\frac{1}{2}\\)x<sup>2<\/sup> &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46701\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 51\" width=\"526\" height=\"553\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-51.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-51-285x300.png 285w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 52.<br \/>\nx<sup>2<\/sup> + y<sup>2<\/sup> = 4<br \/>\ny<sup>2<\/sup> = x + 2<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<b>PROBLEM SOLVING <\/b>The speed s (in miles per hour) of a car can be given by s = \\(\\sqrt{30 f d}\\), where f is the coefficient of friction and d is the stopping distance (in feet). The table shows the coefficient of friction for different surfaces.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40705\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 51\" width=\"355\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-51.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-51-300x145.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\na. Compare the stopping distances of a car traveling 45 miles per hour on the surfaces given in the table.<br \/>\nb. You are driving 35 miles per hour on an icy road when a deer jumps in front of your car. How far away must you begin to brake to avoid hitting the deer? Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46702\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-53.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 53.1\" width=\"554\" height=\"516\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-53.1.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-53.1-300x279.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-53.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 53.2\" width=\"565\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-53.2.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-53.2-300x145.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 54.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> The Beaufort wind scale was devised to measure wind speed. The Beaufort numbers B, which range from 0 to 12, can be modeled by B = 1.69\\(\\sqrt{s+4.25}\\) \u2212 3.55, where s is the wind speed (in miles per hour).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-52.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 52\" width=\"326\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-52.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-52-300x189.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\na. What is the wind speed for B = 0? B = 3?<br \/>\nb. Write an inequality that describes the range of wind speeds represented by the Beaufort model.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<b>USING TOOLS <\/b>Solve the equation x \u2212 4 = \\(\\sqrt{2 x}\\). Then solve the equation x \u2212 4 = \u2212 \\(\\sqrt{2 x}\\).<br \/>\na. How does changing \\(\\sqrt{2 x}\\) to \u2212\\(\\sqrt{2 x}\\) change the solution(s) of the equation?<br \/>\nb. Justify your answer in part (a) using graphs.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-55.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 55.1\" width=\"417\" height=\"425\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-55.1.png 417w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-55.1-294x300.png 294w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46705\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-55.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 55.2\" width=\"575\" height=\"523\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-55.2.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-55.2-300x273.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-55.3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 55.3\" width=\"407\" height=\"341\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-55.3.png 407w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-55.3-300x251.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>Question 56.<br \/>\n<b>MAKING AN ARGUMENT<\/b> Your friend says it is impossible for a radical equation to have two extraneous solutions. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<b>USING STRUCTURE<\/b> Explain how you know the radical equation \\(\\sqrt{x+4}\\) = \u22125 has no real solution without solving it.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46707\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 57\" width=\"584\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-57.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-57-300x30.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 58.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>Use the graph to find the solution of the equation 2\\(\\sqrt{x-4}\\) = \u2212\\(\\sqrt{x-1}\\) + 4. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40707\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 53\" width=\"225\" height=\"177\" \/><br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<b>WRITING<\/b> A company determines that the price p of a product can be modeled by p = 70 \u2212 \\(\\sqrt{0.02 x+1}\\), where x is the number of units of the product demanded per day. Describe the effect that raising the price has on the number of units demanded.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46708\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-59.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 59\" width=\"565\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-59.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-59-300x30.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 60.<br \/>\n<b>THOUGHT PROVOKING<\/b> City officials rope off a circular area to prepare for a concert in the park. They estimate that each person occupies 6 square feet. Describe how you can use a radical inequality to determine the possible radius of the region when P people are expected to attend the concert.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-54.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 54\" width=\"279\" height=\"197\" \/><br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b> The Moeraki Boulders along the coast of New Zealand are stone spheres with radii of approximately 3 feet. A formula for the radius of a sphere is<br \/>\nr = \\(\\frac{1}{2} \\sqrt{\\frac{S}{\\pi}}\\)<br \/>\nwhere S is the surface area of the sphere. Find the surface area of a Moeraki Boulder.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-61.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 61\" width=\"479\" height=\"378\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-61.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-61-300x237.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 62.<br \/>\n<b>PROBLEM SOLVING<\/b> You are trying to determine the height of a truncated pyramid, which cannot be measured directly. The height h and slant height\u2113of the truncated pyramid are related by the formula below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-55.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 55\" width=\"331\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-55.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-55-300x138.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\nIn the given formula, b1 and b2 are the side lengths of the upper and lower bases of the pyramid, respectively. When \u2113 = 5, b<sub>1<\/sub> = 2, and b<sub>2<\/sub> = 4, what is the height of the pyramid?<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<b>REWRITING A FORMULA <\/b>A burning candle has a radius of r inches and was initially h0inches tall. After t minutes, the height of the candle has been reduced to h inches. These quantities are related by the formula<br \/>\nr = \\(\\sqrt{\\frac{k t}{\\pi\\left(h_{0}-h\\right)}}\\)<br \/>\nwhere k is a constant. Suppose the radius of a candle is 0.875 inch, its initial height is 6.5 inches, and k = 0.04.<br \/>\na. Rewrite the formula, solving for h in terms of t.<br \/>\nb. Use your formula in part (a) to determine the height of the candle after burning 45 minutes.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46710\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-63.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 63\" width=\"545\" height=\"273\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-63.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-63-300x150.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Perform the indicated operation. <\/b>(Section 4.2 and Section 4.3)<\/p>\n<p>Question 64.<br \/>\n(x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> + 3x + 1) + (x<sup>4<\/sup> \u2212 7x)<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n(2x<sup>5<\/sup> + x<sup>4<\/sup> \u2212 4x<sup>2<\/sup>) \u2212 (x<sup>5<\/sup> \u2212 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46711\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-65.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 65\" width=\"527\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-65.png 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-65-300x36.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/p>\n<p>Question 66.<br \/>\n(x<sup>3<\/sup> + 2x<sup>2<\/sup> + 1)(x<sup>2<\/sup> + 5)<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n(x<sup>4<\/sup> + 2x<sup>3<\/sup> + 11x<sup>2<\/sup> + 14x \u2212 16) \u00f7 (x + 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46712\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-67.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 67\" width=\"431\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-67.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-67-300x231.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<p><b>Let f(x) = x<sup>3<\/sup> &#8211; 4x<sup>2<\/sup> + 6. Write a rule for g. Describe the graph of g as a transformation of the graph of f.<\/b>(Section 4.7)<\/p>\n<p>Question 68.<br \/>\ng(x) = f(\u2212x) + 4<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\ng(x) = \\(\\frac{1}{2}\\)f(x) \u2212 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-69.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.4 Question 69\" width=\"567\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-69.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.4-Question-69-300x96.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 70.<br \/>\ng(x) = \u2212f(x \u2212 1) + 6<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.5_Performing_Function_Operations\"><\/a>Lesson 5.5 Performing Function Operations<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you use the graphs of two functions to sketch the graph of an arithmetic combination of the two functions?<br \/>\nJust as two real numbers can be combined by the operations of addition, subtraction, multiplication, and division to form other real numbers, two functions can be combined to form other functions. For example, the functions f(x) = 2x \u2212 3 and g(x) = x<sup>2<\/sup> \u2212 1 can be combined to form the sum, difference, product, or quotient of f and g.<br \/>\nf(x) + g(x) = (2x \u2212 3) + (x<sup>2<\/sup> \u2212 1) = x<sup>2<\/sup> + 2x \u2212 4 sum<br \/>\nf(x) \u2212 g(x) = (2x \u2212 3) \u2212 (x<sup>2<\/sup> \u2212 1) = \u2212x<sup>2<\/sup> + 2x \u2212 2 difference<br \/>\nf(x) \u2022 g(x) = (2x \u2212 3)(x<sup>2<\/sup> \u2212 1) = 2x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> \u2212 2x + 3 product<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-56.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 56\" width=\"431\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-56.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-56-300x45.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<p><b>EXPLORATION 1<br \/>\nGraphing the Sum of Two Functions<br \/>\nWork with a partner.<\/b> Use the graphs of f and g to sketch the graph of f + g. Explain your steps.<br \/>\nSample Choose a point on the graph of g. Use a compass or a ruler to measure its distance above or below the x-axis. If above, add the distance to the y-coordinate of the point with the same x-coordinate on the graph of f. If below, subtract the distance. Plot the new point. Repeat this process for several points. Finally, draw a smooth curve through the new points to obtain the graph of f + g.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-57.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 57\" width=\"341\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-57.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-57-300x213.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-58.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 58\" width=\"594\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-58.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-58-300x113.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 2.<br \/>\nHow can you use the graphs of two functions to sketch the graph of an arithmetic combination of the two functions?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-59.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 59\" width=\"253\" height=\"212\" \/><br \/>\nQuestion 3.<br \/>\nCheck your answers in Exploration 1 by writing equations for f and g, adding the functions, and graphing the sum.<\/p>\n<p><b>5.5 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 1.<br \/>\nLet f(x) = \u22122x<sup>2\/3<\/sup> and g(x) = 7x<sup>2\/3<\/sup>. Find (f + g)(x) and (f \u2212 g)(x) and state the domain of each. Then evaluate (f + g)(8) and (f \u2212 g)(8).<\/p>\n<p>Question 2.<br \/>\nLet f(x) = 3x and g(x) = x<sup>1\/5<\/sup>. Find (fg)(x) and (\\(\\frac{f}{g}\\))(x) and state the domain of each. Then evaluate (fg)(32) and (\\(\\frac{f}{g}\\))(32).<\/p>\n<p>Question 3.<br \/>\nLet f(x) = 8x and g(x) = 2x<sup>5\/6<\/sup>. Use a graphing calculator to evaluate (f + g)(x), (f \u2212 g)(x), (fg)(x), and (\\(\\frac{f}{g}\\)) (x) when x = 5. Round your answers to two decimal places.<\/p>\n<p>Question 4.<br \/>\nIn Example 5, explain why you can evaluate (f + g)(3), (f \u2212 g)(3), and (fg)(3) but not (\\(\\frac{f}{g}\\))(3).<\/p>\n<p>Question 5.<br \/>\nUse the answer in Example 6(a) to find the total number of heartbeats over the lifetime of a white rhino when its body mass is 1.7 \u00d7 10<sup>5<\/sup> kilograms.<\/p>\n<h3><a id=\"Performing_Function_Operations_5.5_Exercises\"><\/a>Performing Function Operations 5.5 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING <\/b>Let f and g be any two functions. Describe how you can use f, g, and the four basic operations to create new functions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46714\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 1\" width=\"458\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-1.png 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-1-300x22.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WRITING <\/b>What x-values are not included in the domain of the quotient of two functions?<br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u20136, find (f + g)(x) and (f &#8211; g)(x) and state the domain of each. Then evaluate f + g and f &#8211; g for the given value of x.<\/b><\/p>\n<p>Question 3.<br \/>\nf(x) = \\(-5 \\sqrt[4]{x}\\), g(x) = 19\\(\\sqrt[4]{x}\\); x = 16<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 3\" width=\"580\" height=\"354\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-3.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-3-300x183.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 4.<br \/>\nf(x) = \\(\\sqrt[3]{2 x}\\), g(x) = \u221211\\(\\sqrt[3]{2 x}\\) ; x = \u22124<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nf(x) = 6x \u2212 4x<sup>2<\/sup>\u2212 7x<sup>3<\/sup>, g(x) = 9x<sup>2<\/sup>\u2212 5x; x = \u22121<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 5\" width=\"584\" height=\"388\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-5.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-5-300x199.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 6.<br \/>\nf(x) = 11x + 2x<sup>2<\/sup>, g(x) = \u22127x \u2212 3x<sup>2<\/sup> + 4; x = 2<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 7\u201312, find (fg)(x) and (\\(\\frac{f}{g}\\))(x) and state the domain of each. Then evaluate fg and \\(\\frac{f}{g}\\) for the given value of x.<\/b><\/p>\n<p>Question 7.<br \/>\nf(x) = 2x<sup>3<\/sup>, g(x) = \\(\\sqrt[3]{x}\\) ; x = \u221227<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 7\" width=\"556\" height=\"391\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-7.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-7-300x211.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 8.<br \/>\nf(x) = x<sup>4<\/sup>, g(x) = \\(3 \\sqrt{x}\\) ; x = 4<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nf(x) = 4x, g(x) = 9x<sup>1\/2<\/sup>; x = 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 9\" width=\"582\" height=\"320\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-9.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-9-300x165.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 10.<br \/>\nf(x) = 11x<sup>3<\/sup>, g(x) = 7x<sup>7\/3<\/sup>; x = \u22128<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nf(x) = 7x<sup>3\/2<\/sup>, g(x) =\u221214x<sup>1\/3<\/sup>; x = 64<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 11\" width=\"533\" height=\"387\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-11.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-11-300x218.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 12.<br \/>\nf(x) = 4x<sup>5\/4<\/sup>, g(x) = 2x<sup>1\/2<\/sup>; x = 16<br \/>\nAnswer:<\/p>\n<p><b>USING TOOLS In Exercises 13\u201316, use a graphing calculator to evaluate (f + g)(x), (f \u2212 g)(x), (fg)(x), and (\\(\\frac{f}{g}\\))(x) when x = 5. Round your answers to two decimal places.<\/b><\/p>\n<p>Question 13.<br \/>\nf(x) = 4x<sup>4<\/sup>; g(x) = 24x<sup>1\/3<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 13\" width=\"581\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-13.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-13-300x132.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 14.<br \/>\nf(x) = 7x<sup>5\/3<\/sup>; g(x) = 49x<sup>2\/3<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nf(x) =\u22122x<sup>1\/3<\/sup>; g(x) = 5x<sup>1\/2<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 15\" width=\"571\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-15.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-15-300x94.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = 4x<sup>1\/2<\/sup>; g(x) = 6x<sup>3\/4<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 17 and 18, describe and correct the error in stating the domain.<\/b><\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-60.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 60\" width=\"318\" height=\"102\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-60.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-60-300x96.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 17\" width=\"520\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-17.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-17-300x34.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-61.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 61\" width=\"315\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-61.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-61-300x110.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> From 1990 to 2010, the numbers (in millions) of female F and male M employees from the ages of 16 to 19 in the United States can be modeled by F(t) =\u22120.007t<sup>2<\/sup> + 0.10t + 3.7 and M(t) = 0.0001t<sup>3<\/sup> \u2212 0.009t<sup>2<\/sup> + 0.11t + 3.7, where t is the number of years since 1990.<br \/>\na. Find (F + M)(t).<br \/>\nb. Explain what (F + M)(t) represents.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 19\" width=\"551\" height=\"220\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-19.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-19-300x120.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 20.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> From 2005 to 2009, the numbers of cruise ship departures (in thousands) from around the world W and Florida F can be modeled by the equations<br \/>\nW(t) = \u22125.8333t<sup>3<\/sup> + 17.43t<sup>2<\/sup> + 509.1t + 11496<br \/>\nF(t) = 12.5t<sup>3<\/sup> \u2212 60.29t<sup>2<\/sup> + 136.6t + 4881<br \/>\nwhere t is the number of years since 2005.<br \/>\na. Find (W \u2212 F )(t).<br \/>\nb. Explain what (W \u2212 F )(t) represents.<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<b>MAKING AN ARGUMENT <\/b>Your friend claims that the addition of functions and the multiplication of functions are commutative. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 21\" width=\"583\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-21.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-21-300x58.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 22.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>The graphs of the functions f(x) = 3x<sup>2<\/sup> \u2212 2x \u2212 1 and g(x) = 3x + 4 are shown. Which graph represents the function f + g? the function f \u2212 g? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-62.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 62\" width=\"372\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-62.png 372w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-62-300x244.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<b>REASONING <\/b>The table shows the outputs of the two functions f and g. Use the table to evaluate (f + g)(3), (f \u2212 g)(1), (fg)(2), and (\\(\\frac{f}{g}\\))(0).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-63.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 63\" width=\"289\" height=\"115\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 23\" width=\"439\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-23.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-23-300x115.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/p>\n<p>Question 24.<br \/>\n<b>THOUGHT PROVOKING<\/b> Is it possible to write two functions whose sum contains radicals, but whose product does not? Justify your answers.<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b> A triangle is inscribed in a square, as shown. Write and simplify a function r in terms of x that represents the area of the shaded region.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-64.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 64\" width=\"119\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 25\" width=\"403\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-25.png 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-25-300x106.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Question 26.<br \/>\n<b>REWRITING A FORMULA <\/b>For a mammal that weighs w grams, the volume b (in milliliters) of air breathed in and the volume d (in milliliters) of \u201cdead space\u201d (the portion of the lungs not filled with air) can be modeled by<br \/>\nb(w) = 0.007w and d(w) = 0.002w.<br \/>\nThe breathing rate r (in breaths per minute) of a mammal that weighs w grams can be modeled by<br \/>\nr(w) = \\(\\frac{1.1 w^{0.734}}{b(w)-d(w)}\\).<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<b>PROBLEM SOLVING <\/b>A mathematician at a lake throws a tennis ball from point A along the water\u2019s edge to point B in the water, as shown. His dog, Elvis, first runs along the beach from point A to point D and then swims to fetch the ball at point B.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40731\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-65.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 65\" width=\"276\" height=\"157\" \/><br \/>\na. Elvis runs at a speed of about 6.4 meters per second. Write a function r in terms of x that represents the time he spends running from point A to point D. Elvis swims at a speed of about 0.9 meter per second. Write a function s in terms of x that represents the time he spends swimming from point D to point B.<br \/>\nb. Write a function t in terms of x that represents the total time Elvis spends traveling from point A to point D to point B.<br \/>\nc. Use a graphing calculator to graph t. Find the value of x that minimizes t. Explain the meaning of this value.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 27\" width=\"580\" height=\"403\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-27.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-27-300x208.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Solve the literal equation for n. <\/b>(Skills Review Handbook)<\/p>\n<p>Question 28.<br \/>\n3xn \u2212 9 = 6y<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n5z = 7n + 8nz<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 29\" width=\"222\" height=\"123\" \/><\/p>\n<p>Question 30.<br \/>\n3nb = 5n \u2212 6z<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n\\(\\frac{3+4 n}{n}\\) = 7b<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 31\" width=\"234\" height=\"212\" \/><\/p>\n<p><b>Determine whether the relation is a function. Explain. <\/b>(Skills Review Handbook)<\/p>\n<p>Question 32.<br \/>\n(3, 4), (4, 6), (1, 4), (2, \u22121)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n(\u22121, 2), (3, 7), (0, 2), (\u22121, \u22121)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46731\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 33\" width=\"539\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-33.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-33-300x20.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 34.<br \/>\n(1, 6), (7, \u22123), (4, 0), (3, 0)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n(3, 8), (2, 5), (9, 5), (2, \u22123)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.5 Question 35\" width=\"511\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-35.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.5-Question-35-300x21.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<h3><a id=\"Lesson_5.6_Inverse_of_a_Function\"><\/a>Lesson 5.6 Inverse of a Function<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you sketch the graph of the inverse of a function?<\/p>\n<p><b>EXPLORATION 1<br \/>\nGraphing Functions and Their Inverses<br \/>\nWork with a partner. <\/b>Each pair of functions are inverses of each other. Use a graphing calculator to graph f and g in the same viewing window. What do you notice about the graphs?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-65.1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 65.1\" width=\"247\" height=\"197\" \/><br \/>\na. f(x) = 4x + 3<br \/>\ng(x) = \\(\\frac{x-3}{4}\\)<br \/>\nb. f(x) = x<sup>3<\/sup> + 1<br \/>\ng(x) = \\(\\sqrt[3]{x-1}\\)<br \/>\nc. f(x) = \\(\\sqrt{x-3}[latex]<br \/>\ng(x) = x<sup>2<\/sup> + 3, x \u2265 0<br \/>\nd. f(x) = [latex]\\frac{4 x+4}{x+5}\\)<br \/>\ng(x) = \\(\\frac{4-5 x}{x-4}\\)<\/p>\n<p><b>EXPLORATION 2<br \/>\nSketching Graphs of Inverse Functions<br \/>\nWork with a partner.<\/b> Use the graph of f to sketch the graph of g, the inverse function of f, on the same set of coordinate axes. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-66.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 66\" width=\"619\" height=\"451\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-66.png 619w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-66-300x219.png 300w\" sizes=\"(max-width: 619px) 100vw, 619px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you sketch the graph of the inverse of a function?<\/p>\n<p>Question 4.<br \/>\nIn Exploration 1, what do you notice about the relationship between the equations of f and g? Use your answer to find g, the inverse function of<br \/>\nf(x) = 2x \u2212 3.<br \/>\nUse a graph to check your answer.<\/p>\n<p><b>5.6 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve y = f(x) for x. Then find the input(s) when the output is 2.<\/b><\/p>\n<p>Question 1.<br \/>\nf(x) = x \u2212 2<\/p>\n<p>Question 2.<br \/>\nf(x) = 2x<sup>2<\/sup><\/p>\n<p>Question 3.<br \/>\nf(x) = \u2212x<sup>3<\/sup> + 3<\/p>\n<p><b>Find the inverse of the function. Then graph the function and its inverse.<\/b><\/p>\n<p>Question 4.<br \/>\nf(x) = 2x<\/p>\n<p>Question 5.<br \/>\nf(x) = \u2212x + 1<\/p>\n<p>Question 6.<br \/>\nf(x) = \\(\\frac{1}{3}\\)x \u2212 2<\/p>\n<p><b>Find the inverse of the function. Then graph the function and its inverse.<\/b><\/p>\n<p>Question 7.<br \/>\nf(x) = \u2212x<sup>2<\/sup>, x \u2264 0<\/p>\n<p>Question 8.<br \/>\nf(x) = \u2212x<sup>3<\/sup> + 4<\/p>\n<p>Question 9.<br \/>\nf(x) = \\(\\sqrt{x+2}\\)<\/p>\n<p><b>Determine whether the functions are inverse functions.<\/b><\/p>\n<p>Question 10.<br \/>\nf(x) = x + 5, g(x) = x \u2212 5<\/p>\n<p>Question 11.<br \/>\nf(x) = 8x<sup>3<\/sup>, g(x) = \\(\\sqrt[3]{2 x}\\)<\/p>\n<p>Question 12.<br \/>\nThe distance d (in meters) that a dropped object falls in t seconds on Earth is represented by d = 4.9t<sup>2<\/sup>. Find the inverse of the function. How long does it take an object to fall 50 meters?<\/p>\n<h3><a id=\"Inverse_of_a_Function_5.6_Exercises\"><\/a>Inverse of a Function 5.6 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>VOCABULARY <\/b>In your own words, state the definition of inverse functions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 1\" width=\"487\" height=\"30\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-1.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-1-300x18.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WRITING<\/b> Explain how to determine whether the inverse of a function is also a function.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<b>COMPLETE THE SENTENCE<\/b> Functions f and g are inverses of each other provided that f(g(x)) = ____ and g(f(x)) = ____.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 3\" width=\"540\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-3.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-3-300x32.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>DIFFERENT WORDS, SAME QUESTION <\/b>Which is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-67.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 67\" width=\"720\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-67.png 720w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-67-300x64.png 300w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 5\u201312, solve y = f(x) for x. Then find the input(s) when the output is -3.<\/b><\/p>\n<p>Question 5.<br \/>\nf(x) = 3x + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 5\" width=\"399\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-5.png 399w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-5-300x188.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>Question 6.<br \/>\nf(x) = \u22127x \u2212 2<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nf(x) = \\(\\frac{1}{2}\\)x \u2212 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 7\" width=\"383\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-7.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-7-300x247.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n<p>Question 8.<br \/>\nf(x) = \u2212\\(\\frac{2}{3}\\)x + 1<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nf(x) = 3x<sup>3<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 9\" width=\"403\" height=\"353\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-9.png 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-9-300x263.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Question 10.<br \/>\nf(x) = 2x<sup>4<\/sup> \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nf(x) = (x \u2212 2)<sup>2<\/sup> \u2212 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 11\" width=\"424\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-11.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-11-300x246.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>Question 12.<br \/>\nf(x) = (x \u2212 5)<sup>3<\/sup> \u2212 1<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 13\u201320, find the inverse of the function. Then graph the function and its inverse.<\/b><\/p>\n<p>Question 13.<br \/>\nf(x) = 6x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-13.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 13.1\" width=\"586\" height=\"406\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-13.1.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-13.1-300x208.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-13.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 13.2\" width=\"222\" height=\"199\" \/><\/p>\n<p>Question 14.<br \/>\nf(x) = \u22123x<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nf(x) = \u22122x + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-15.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 15.1\" width=\"591\" height=\"499\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-15.1.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-15.1-300x253.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46742\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-15.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 15.2\" width=\"303\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-15.2.png 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-15.2-300x281.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = 6x \u2212 3<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nf(x) = \u2212\\(\\frac{1}{2}\\)x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-17.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 17.1\" width=\"593\" height=\"506\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-17.1.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-17.1-300x256.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-17.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 17.2\" width=\"305\" height=\"287\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-17.2.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-17.2-300x282.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 18.<br \/>\nf(x) = \\(\\frac{1}{3}\\)x \u2212 1<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nf(x) = \\(\\frac{2}{3}\\)x \u2212 \\(\\frac{1}{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-19.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 19.1\" width=\"569\" height=\"299\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-19.1.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-19.1-300x158.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-19.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 19.2\" width=\"487\" height=\"464\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-19.2.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-19.2-300x286.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 20.<br \/>\nf(x) = \u2212\\(\\frac{4}{5}\\)x + \\(\\frac{1}{5}\\)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<b>COMPARING METHODS <\/b>Find the inverse of the function f(x) = \u22123x + 4 by switching the roles of x and y and solving for y. Then find the inverse of the function f by using inverse operations in the reverse order. Which method do you prefer? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 21\" width=\"570\" height=\"368\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-21.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-21-300x194.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 22.<br \/>\n<b>REASONING <\/b>Determine whether each pair of functions f and g are inverses. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-68.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 68\" width=\"322\" height=\"521\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-68.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-68-185x300.png 185w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 23\u201328, find the inverse of the function. Then graph the function and its inverse.<\/b><\/p>\n<p>Question 23.<br \/>\nf(x) = 4x<sup>2<\/sup>, x \u2264 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 23\" width=\"570\" height=\"478\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-23.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-23-300x252.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 24.<br \/>\nf(x) = 9x<sup>2<\/sup>, x \u2264 0<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nf(x) = (x \u2212 3)<sup>3<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 25\" width=\"338\" height=\"500\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-25.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-25-203x300.png 203w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Question 26.<br \/>\nf(x) = (x + 4)<sup>3<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nf(x) = 2x<sup>4<\/sup>, x \u2265 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 27\" width=\"564\" height=\"441\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-27.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-27-300x235.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 28.<br \/>\nf(x) = \u2212x<sup>6<\/sup>, x \u2265 0<br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 29 and 30, describe and correct the error in finding the inverse of the function.<\/b><\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-69.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 69\" width=\"278\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 29\" width=\"566\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-29.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-29-300x124.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-70.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 70\" width=\"286\" height=\"199\" \/><br \/>\nAnswer:<\/p>\n<p><b>USING TOOLS In Exercises 31\u201334, use the graph to determine whether the inverse of f is a function. Explain your reasoning.<\/b><\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-71.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 71\" width=\"201\" height=\"154\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 31\" width=\"556\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-31.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-31-300x36.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-72.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 72\" width=\"203\" height=\"149\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-73.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 73\" width=\"196\" height=\"152\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 33\" width=\"558\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-33.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-33-300x38.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-74.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 74\" width=\"204\" height=\"142\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 35\u201346, determine whether the inverse of f is a function. Then find the inverse.<\/b><\/p>\n<p>Question 35.<br \/>\nf(x) = x<sup>3<\/sup>\u00a0\u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 35\" width=\"548\" height=\"351\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-35.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-35-300x192.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 36.<br \/>\nf(x) = \u2212x<sup>3<\/sup> + 3<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\nf(x) = \\(\\sqrt{x+4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 37\" width=\"573\" height=\"380\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-37.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-37-300x199.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 38.<br \/>\nf(x) = \\(\\sqrt{x-6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nf(x) = \\(2 \\sqrt[3]{x-5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 39\" width=\"581\" height=\"447\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-39.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-39-300x231.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 40.<br \/>\nf(x) = 2x<sup>2<\/sup> \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nf(x) = x<sup>4<\/sup> + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 41\" width=\"582\" height=\"460\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-41.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-41-300x237.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 42.<br \/>\nf(x) = 2x<sup>3<\/sup> \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nf(x) = \\(3 \\sqrt[3]{x+1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 43\" width=\"561\" height=\"485\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-43.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-43-300x259.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 44.<br \/>\nf(x) = \\(-\\sqrt[3]{\\frac{2 x+4}{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\nf(x) = \\(\\frac{1}{2}\\)x<sup>5<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 45\" width=\"566\" height=\"591\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-45.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-45-287x300.png 287w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 46.<br \/>\nf(x) = \\(-3 \\sqrt{\\frac{4 x-7}{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<b>WRITING EQUATIONS<\/b> What is the inverse of the function whose graph is shown?<br \/>\nA. g(x) = \\(\\frac{3}{2}\\)x \u2212 6<br \/>\nB. g(x) = \\(\\frac{3}{2}\\)x + 6<br \/>\nC. g(x) = \\(\\frac{2}{3}\\)x \u2212 6<br \/>\nD. g(x) = \\(\\frac{2}{3}\\)x + 12<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40742\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-75.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 75\" width=\"217\" height=\"169\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 47\" width=\"559\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-47.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-47-300x18.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>WRITING EQUATIONS <\/b>What is the inverse of f(x) = \u2212\\(-\\frac{1}{64}\\)x<sup>3<\/sup>?<br \/>\nA. g(x) = \u22124x<sup>3<\/sup><br \/>\nB. g(x) = 4\\(\\sqrt[3]{x}\\)<br \/>\nC. g(x) = \u22124\\(\\sqrt[3]{x}\\)<br \/>\nD. g(x) = \\(\\sqrt[3]{-4 x}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 49\u201352, determine whether the functions are inverses.<\/b><\/p>\n<p>Question 49.<br \/>\nf(x) = 2x \u2212 9, g(x) = x \u2014 2 + 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 49\" width=\"317\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-49.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-49-300x245.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/p>\n<p>Question 50.<br \/>\nf(x) = \\(\\frac{x-3}{4}\\), g(x) = 4x + 3<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\nf(x) = \\(\\sqrt[5]{\\frac{x+9}{5}}\\), g(x) = 5x<sup>5<\/sup> \u2212 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-51.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 51.1\" width=\"332\" height=\"325\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-51.1.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-51.1-300x294.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-51.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 51.2\" width=\"339\" height=\"316\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-51.2.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-51.2-300x280.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p>Question 52.<br \/>\nf(x) = 7x<sup>3\/2<\/sup> \u2212 4, g(x) = (\\(\\frac{x+4}{7}\\))<sup>3\/2<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>The maximum hull speed v (in knots) of a boat with a displacement hull can be approximated by v = 1.34\\(\\sqrt{\\ell}\\), where \u2113 is the waterline length (in feet) of the boat. Find the inverse function. What waterline length is needed to achieve a maximum speed of 7.5 knots?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-76.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 76\" width=\"295\" height=\"157\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-53.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 53.1\" width=\"409\" height=\"347\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-53.1.png 409w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-53.1-300x255.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><\/p>\n<p>Question 54.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> Elastic bands can be used for exercising to provide a range of resistance. The resistance R (in pounds) of a band can be modeled by R = \\(\\frac{3}{8}\\)L \u2212 5, where L is the total length (in inches) of the stretched band. Find the inverse function. What length of the stretched band provides 19 pounds of resistance?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-77.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 77\" width=\"319\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-77.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-77-300x187.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<\/p>\n<p><b>ANALYZING RELATIONSHIPS In Exercises 55\u201358, match the graph of the function with the graph of its inverse.<\/b><\/p>\n<p>Question 55.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-78.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 78\" width=\"183\" height=\"151\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 55\" width=\"549\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-55.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-55-300x33.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 56.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-79.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 79\" width=\"196\" height=\"149\" \/><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-80.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 80\" width=\"180\" height=\"148\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 57\" width=\"551\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-57.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-57-300x31.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 58.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-81.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 81\" width=\"187\" height=\"150\" \/><br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-82.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 82\" width=\"408\" height=\"352\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-82.png 408w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-82-300x259.png 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p>Question 59.<br \/>\n<b>REASONING <\/b>You and a friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add 3. Your friend\u2019s final answer is 53. What was the original number chosen? Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-59.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 59\" width=\"498\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-59.png 498w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-59-300x78.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/p>\n<p>Question 60.<br \/>\n<b>MAKING AN ARGUMENT <\/b>Your friend claims that every quadratic function whose domain is restricted to nonnegative values has an inverse function. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<b>PROBLEM SOLVING <\/b>When calibrating a spring scale, you need to know how far the spring stretches for various weights. Hooke\u2019s Law states that the length a spring stretches is proportional to the weight attached to it. A model for one scale is \u2113 = 0.5w + 3, where\u2113 is the total length (in inches) of the stretched spring and w is the weight (in pounds) of the object.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-83.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 83\" width=\"219\" height=\"225\" \/><br \/>\na. Find the inverse function. Describe what it represents.<br \/>\nb. You place a melon on the scale, and the spring stretches to a total length of 5.5 inches. Determine the weight of the melon.<br \/>\nc. Verify that the function \u2113 = 0.5w + 3 and the inverse model in part (a) are inverse functions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-61.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 61.1\" width=\"514\" height=\"474\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-61.1.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-61.1-300x277.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-61.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 61.2\" width=\"371\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-61.2.png 371w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-61.2-300x171.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/p>\n<p>Question 62.<br \/>\n<b>THOUGHT PROVOKING <\/b>Do functions of the form y = x<sup>m\/n<\/sup>, where m and n are positive integers, have inverse functions? Justify your answer with examples.<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<b>PROBLEM SOLVING<\/b> At the start of a dog sled race in Anchorage, Alaska, the temperature was 5\u00b0C. By the end of the race, the temperature was \u221210\u00b0C. The formula for converting temperatures from degrees Fahrenheit F to degrees Celsius C is C = \\(\\frac{5}{9}\\)(F \u2212 32).<br \/>\na. Find the inverse function. Describe what it represents.<br \/>\nb. Find the Fahrenheit temperatures at the start and end of the race.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-84.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 84\" width=\"199\" height=\"162\" \/><br \/>\nc. Use a graphing calculator to graph the original function and its inverse. Find the temperature that is the same on both temperature scales.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-63.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 63.1\" width=\"575\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-63.1.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-63.1-300x259.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 64.<br \/>\n<b>PROBLEM SOLVING<\/b> The surface area A (in square meters) of a person with a mass of 60 kilograms can be approximated by A = 0.2195h<sup>0.3964<\/sup>, where h is the height (in centimeters) of the person.<br \/>\na. Find the inverse function. Then estimate the height of a 60-kilogram person who has a body surface area of 1.6 square meters.<br \/>\nb. Verify that function A and the inverse model in part (a) are inverse functions.<br \/>\nAnswer:<\/p>\n<p><b>USING STRUCTURE In Exercises 65\u201368, match the function with the graph of its inverse.<\/b><\/p>\n<p>Question 65.<br \/>\nf(x) = \\(\\sqrt[3]{x-4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-65.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 65.1\" width=\"268\" height=\"365\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-65.1.png 268w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-65.1-220x300.png 220w\" sizes=\"(max-width: 268px) 100vw, 268px\" \/><\/p>\n<p>Question 66.<br \/>\nf(x) = \\(\\sqrt[3]{x+4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\nf(x) = \\(\\sqrt{x+1}\\) &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-67.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 67.1\" width=\"574\" height=\"270\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-67.1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-67.1-300x141.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 68.<br \/>\nf(x) = \\(\\sqrt{x-1}\\) + 3<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-85.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 5 Rational Exponents and Radical Functions 85\" width=\"375\" height=\"318\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-85.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-85-300x254.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/p>\n<p>Question 69.<br \/>\n<b>DRAWING CONCLUSIONS <\/b>Determine whether the statement is true or false. Explain your reasoning.<br \/>\na. If f(x) = x<sup>n<\/sup> and n is a positive even integer, then the inverse of f is a function.<br \/>\nb. If f(x) = x<sup>n<\/sup> and n is a positive odd integer, then the inverse of f is a function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-69.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 69.1\" width=\"584\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-69.1.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-69.1-300x64.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 70.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> The graph of the function f is shown. Name three points that lie on the graph of the inverse of f. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40708\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-86.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 86\" width=\"187\" height=\"178\" \/><br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n<b>ABSTRACT REASONING<\/b> Show that the inverse of any linear function f(x) = mx + b, where m \u2260 0, is also a linear function. Identify the slope and y-intercept of the graph of the inverse function in terms of m and b.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-71.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 71\" width=\"524\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-71.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-71-300x171.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p>Question 72.<br \/>\n<b>CRITICAL THINKING <\/b>Consider the function f(x) = \u2212x.<br \/>\na. Graph f(x) = \u2212x and explain why it is its own inverse. Also, verify that f(x) = \u2212x is its own inverse algebraically.<br \/>\nb. Graph other linear functions that are their own inverses. Write equations of the lines you graphed.<br \/>\nc. Use your results from part (b) to write a general equation describing the family of linear functions that are their own inverses.<br \/>\nAnswer:<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Simplify the expression. Write your answer using only positive exponents.<\/b>(Skills Review Handbook)<\/p>\n<p>Question 73.<br \/>\n(\u22123)<sup>\u22123<br \/>\n<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-73.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 73\" width=\"164\" height=\"118\" \/><\/p>\n<p>Question 74.<br \/>\n2<sup>3<\/sup> \u2022 2<sup>2<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\n\\(\\frac{4^{5}}{4^{3}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-75.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 75\" width=\"157\" height=\"63\" \/><\/p>\n<p>Question 76.<br \/>\n(\\(\\frac{2}{3}\\))<sup>4<br \/>\n<\/sup><br \/>\nAnswer:<\/p>\n<p><b>Describe the x-values for which the function is increasing, decreasing, positive, and negative.<\/b><\/p>\n<p>Question 77.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-87.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 87\" width=\"178\" height=\"151\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-77.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 77\" width=\"559\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-77.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-77-300x49.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 78.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40710\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-88.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 88\" width=\"188\" height=\"160\" \/><br \/>\nAnswer:<\/p>\n<p>Question 79.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40711\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-89.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 89\" width=\"158\" height=\"182\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-79.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions 5.6 Question 79\" width=\"538\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-79.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-5.6-Question-79-300x61.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<h3><a id=\"Rational_Exponents_and_Radical_Functions_Performance_Task\"><\/a>Rational Exponents and Radical Functions Performance Task: Turning the Tables<\/h3>\n<p><b>5.4\u20135.6 What Did You Learn?<\/b><\/p>\n<p><b>Core Vocabulary<\/b><br \/>\nradical equation, p. 262<br \/>\nextraneous solutions, p. 263<br \/>\ninverse functions, p. 277<\/p>\n<p><b>Core Concepts<br \/>\nSection 5.4<\/b><br \/>\nSolving Radical Equations, p. 262<br \/>\nSolving Radical Inequalities, p. 265<\/p>\n<p><b>Section 5.5<\/b><br \/>\nOperations on Functions, p. 270<\/p>\n<p><b>Section 5.6<\/b><br \/>\nExploring Inverses of Functions, p. 276<br \/>\nInverses of Nonlinear Functions, p. 278<br \/>\nHorizontal Line Test, p. 278<\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nHow did you find the endpoints of the range in part (b) of Exercise 54 on page 267?<\/p>\n<p>Question 2.<br \/>\nHow did you use structure in Exercise 57 on page 268?<\/p>\n<p>Question 3.<br \/>\nHow can you evaluate the reasonableness of the results in Exercise 27 on page 274?<\/p>\n<p>Question 4.<br \/>\nHow can you use a graphing calculator to check your answers in Exercises 49\u201352 on page 282?<\/p>\n<p><b>Performance Task<\/b><\/p>\n<p><b>Turning the Tables<\/b><\/p>\n<p>In this chapter, you have used properties of rational exponents and functions to find an answer to the problem. Using those same properties, can you find a problem to the answer? How many problems can you find?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40712\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-90.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 90\" width=\"458\" height=\"346\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-90.png 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-90-300x227.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nTo explore the answers to these questions and more, go to BigIdeasMath.com<\/p>\n<h3><a id=\"Rational_Exponents_and_Radical_Functions_Chapter_Review\"><\/a>Rational Exponents and Radical Functions Chapter Review<\/h3>\n<p><b>Evaluate the expression without using a calculator.<\/b><\/p>\n<p>Question 1.<br \/>\n8<sup>7\/3<\/sup><\/p>\n<p>Question 2.<br \/>\n9<sup>5\/2<\/sup><\/p>\n<p>Question 3.<br \/>\n(\u221227)<sup>\u22122\/3<\/sup><\/p>\n<p><b>Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate.<\/b><\/p>\n<p>Question 4.<br \/>\nx<sup>5<\/sup> + 17 = 35<\/p>\n<p>Question 5.<br \/>\n7x<sup>3<\/sup> = 189<\/p>\n<p>Question 6.<br \/>\n(x + 8)<sup>4<\/sup> = 16<\/p>\n<p><b>Simplify the expression.<\/b><\/p>\n<p>Question 7.<br \/>\n(\\(\\frac{6^{1 \/ 5}}{6^{2 \/ 5}}\\))<sup>3<\/sup><\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt[4]{32} \\cdot \\sqrt[4]{8}\\)<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{1}{2-\\sqrt[4]{9}}\\)<\/p>\n<p>Question 10.<br \/>\n\\(4 \\sqrt[5]{8}\\) + \\(3 \\sqrt[5]{8}\\)<\/p>\n<p>Question 11.<br \/>\n\\(2 \\sqrt{48}\\) &#8211; \\(\\sqrt{3}\\)<\/p>\n<p>Question 12.<br \/>\n(\\(5^{2 \/ 3} \\cdot 2^{3 \/ 2}\\))<sup>1\/2<\/sup><\/p>\n<p><b>Simplify the expression. Assume all variables are positive.<\/b><\/p>\n<p>Question 13.<br \/>\n\\(\\sqrt[3]{125 z^{9}}\\)<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{2^{1 \/ 4} z^{5 \/ 4}}{6 z}\\)<\/p>\n<p>Question 15.<br \/>\n\\(\\sqrt{10 z^{5}}-z^{2} \\sqrt{40 z}\\)<\/p>\n<p><b>Describe the transformation of f represented by g. Then graph each function.<\/b><\/p>\n<p>Question 16.<br \/>\nf(x) = \\(\\sqrt{x}\\), g(x) = \u22122\\(\\sqrt{x}\\)<\/p>\n<p>Question 17.<br \/>\nf(x) = \\(\\sqrt[3]{x}\\), g(x) = \\(\\sqrt[3]{-x}\\) \u2212 6<\/p>\n<p>Question 18.<br \/>\nLet the graph of g be a reflection in the y-axis, followed by a translation 7 units to the right of the graph of f(x) = \\(\\sqrt[3]{x}\\). Write a rule for g.<\/p>\n<p>Question 19.<br \/>\nUse a graphing calculator to graph 2y<sup>2<\/sup> = x \u2212 8. Identify the vertex and the direction that the parabola opens.<\/p>\n<p>Question 20.<br \/>\nUse a graphing calculator to graph x<sup>2<\/sup> + y<sup>2<\/sup> = 81. Identify the radius and the intercepts.<\/p>\n<p><b>Solve the equation. Check your solution.<\/b><\/p>\n<p>Question 21.<br \/>\n\\(4 \\sqrt[3]{2 x+1}\\) = 20<\/p>\n<p>Question 22.<br \/>\n\\(\\sqrt{4 x-4}\\) = \\(\\sqrt{5 x-1}\\) &#8211; 1<\/p>\n<p>Question 23.<br \/>\n(6x)<sup>2\/3<\/sup> = 36<\/p>\n<p><b>Solve the inequality.<\/b><\/p>\n<p>Question 24.<br \/>\n\\(5 \\sqrt{x}\\) + 2 &gt; 17<\/p>\n<p>Question 25.<br \/>\n\\(2 \\sqrt{x-8}\\) &lt; 24<\/p>\n<p>Question 26.<br \/>\n7\\(\\sqrt[3]{x-3}\\) \u2265 21<\/p>\n<p>Question 27.<br \/>\nIn a tsunami, the wave speeds (in meters per second) can be modeled by s(d ) = \\(\\sqrt{9.8 d}\\), where d is the depth (in meters) of the water. Estimate the depth of the water when the wave speed is 200 meters per second.<\/p>\n<p>Question 28.<br \/>\nLet f(x) = 2\\(\\sqrt{3-x}\\) and g(x) = 4\\(\\sqrt[3]{3-x}\\). Find (fg)(x) and (\\(\\frac{f}{g}\\))(x) and state the domain of each. Then evaluate(fg)(2) and (\\(\\frac{f}{g}\\))(2).<\/p>\n<p>Question 29.<br \/>\nLet f(x) = 3x<sup>2<\/sup> + 1 and g(x) = x + 4. Find (f + g)(x) and (f \u2212 g)(x) and state the domain of each. Then evaluate (f + g)(\u22125) and (f \u2212 g)(\u22125).<\/p>\n<p>Question 30.<br \/>\nf(x) = \u2212\\(\\frac{1}{2}\\)x + 10<\/p>\n<p>Question 31.<br \/>\nf(x) = x<sup>2<\/sup> + 8, x \u2265 0<\/p>\n<p>Question 32.<br \/>\nf(x) = \u2212x<sup>3<\/sup> \u2212 9<\/p>\n<p>Question 33.<br \/>\nf(x) = 3\\(\\sqrt{x}\\) + 5<\/p>\n<p><b>Determine whether the functions are inverse functions.<\/b><\/p>\n<p>Question 34.<br \/>\nf(x) = 4(x \u2212 11)<sup>2<\/sup>, g(x) = \\(\\frac{1}{4}\\)(x + 11)<sup>2<\/sup><\/p>\n<p>Question 35.<br \/>\nf(x) = \u22122x + 6, g(x) = \u2212\\(\\frac{1}{2}\\)x + 3<\/p>\n<p>Question 36.<br \/>\nOn a certain day, the function that gives U.S. dollars in terms of British pounds is d = 1.587p, where d represents U.S. dollars and p represents British pounds. Find the inverse function. Then find the number of British pounds equivalent to 100 U.S. dollars.<\/p>\n<h3><a id=\"Rational_Exponents_and_Radical_Functions_Chapter_Test\"><\/a>Rational Exponents and Radical Functions Chapter Test<\/h3>\n<p>Question 1.<br \/>\nSolve the inequality \\(\\) \u2212 2 \u2264 13 and the equation 5\\(\\) \u2212 2 = 13. Describe the similarities and differences in solving radical equations and radical inequalities.<\/p>\n<p><b>Describe the transformation of f represented by g. Then write a rule for g.<\/b><\/p>\n<p>Question 2.<br \/>\nf(x) = \\(\\sqrt{x}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-92.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 92\" width=\"188\" height=\"148\" \/><\/p>\n<p>Question 3.<br \/>\nf(x) = \\(\\sqrt[3]{x}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40714\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-93.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 93\" width=\"192\" height=\"155\" \/><\/p>\n<p>Question 4.<br \/>\nf(x) = \\(\\sqrt[5]{x}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-94.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 94\" width=\"188\" height=\"152\" \/><\/p>\n<p><b>Simplify the expression. Explain your reasoning.<\/b><\/p>\n<p>Question 5.<br \/>\n64<sup>2\/3<\/sup><\/p>\n<p>Question 6.<br \/>\n(\u221227)<sup>5\/3<\/sup><\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt[4]{48 x y^{11} z^{3}}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{\\sqrt[3]{256}}{\\sqrt[3]{32}}\\)<\/p>\n<p>Question 9.<br \/>\nWrite two functions whose graphs are translations of the graph of y = \\(\\sqrt{x}\\). The first function should have a domain of x \u2265 4. The second function should have a range of y \u2265 \u22122.<\/p>\n<p>Question 10.<br \/>\nIn bowling, a handicap is a change in score to adjust for differences in the abilities of players. You belong to a bowling league in which your handicap h is determined using the formula h = 0.9(200 \u2212 a), where a is your average score. Find the inverse of the model. Then find the average for a bowler whose handicap is 36.<\/p>\n<p>Question 11.<br \/>\nThe basal metabolic rate of an animal is a measure of the amount of calories burned at rest for basic functioning. Kleiber\u2019s law states that an animal\u2019s basal metabolic rate R (in kilocalories per day) can be modeled by R = 73.3w<sup>3\/4<\/sup>, where w is the mass (in kilograms) of the animal. Find the basal metabolic rates of each animal in the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-95.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 95\" width=\"269\" height=\"182\" \/><\/p>\n<p>Question 12.<br \/>\nLet f(x) = 6x<sup>3\/5<\/sup> and g(x) = \u2212x<sup>3\/5<\/sup>. Find (f + g)(x) and (f \u2212 g)(x) and state the domain of each. Then evaluate (f + g)(32) and (f \u2212 g)(32).<\/p>\n<p>Question 13.<br \/>\nLet f(x) = \\(\\frac{1}{2}\\)x<sup>3\/4<\/sup> and g(x) = 8x. Find (fg)(x) and (\\(\\frac{f}{g}\\))(x) and state the domain of each. Then evaluate (fg)(16) and (\\(\\frac{f}{g}\\))(16).<\/p>\n<p>Question 14.<br \/>\nA football player jumps to catch a pass. The maximum height h (in feet) of the player above the ground is given by the function h = \\(\\frac{1}{64}\\)s<sup>2<\/sup>, where s is the initial speed (in feet per second) of the player. Find the inverse of the function. Use the inverse to find the initial speed of the player shown. Verify that the functions are inverse functions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-96.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 96\" width=\"198\" height=\"241\" \/><\/p>\n<h3><a id=\"Rational_Exponents_and_Radical_Functions_Cumulative_Assessment\"><\/a>Rational Exponents and Radical Functions Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nIdentify three pairs of equivalent expressions. Assume all variables are positive. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-97.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 5 Rational Exponents and Radical Functions 97\" width=\"322\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-97.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-5-Rational-Exponents-and-Radical-Functions-97-300x116.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><\/p>\n<p>Question 2.<br \/>\nThe graph represents the function <img loading=\"lazy\" class=\"alignnone size-full wp-image-40754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-98.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 5 Rational Exponents and Radical Functions 98\" width=\"139\" height=\"42\" \/>. Choose the correct values to complete the function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-98.1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 5 Rational Exponents and Radical Functions 98.1\" width=\"448\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-98.1.png 448w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-98.1-300x127.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><\/p>\n<p>Question 3.<br \/>\nIn rowing, the boat speed s (in meters per second) can be modeled by s= 4.62\\(\\sqrt[9]{n}\\), where n is the number of rowers.<br \/>\na. Find the boat speeds for crews of 2 people, 4 people, and 8 people.<br \/>\nb. Does the boat speed double when the number of rowers doubles? Explain.<br \/>\nc. Find the time (in minutes) it takes each crew in part (a) to complete a 2000-meter race.<\/p>\n<p>Question 4.<br \/>\nA polynomial function fits the data in the table. Use finite differences to find the degree of the function and complete the table. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-99.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 5 Rational Exponents and Radical Functions 99\" width=\"423\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-99.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-99-300x61.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p>\n<p>Question 5.<br \/>\nThe area of the triangle is 42 square inches. Find the value of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-100.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 5 Rational Exponents and Radical Functions 100\" width=\"232\" height=\"135\" \/><\/p>\n<p>Question 6.<br \/>\nWhich equations are represented by parabolas? Which equations are functions? Place check marks in the appropriate spaces. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-101.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 5 Rational Exponents and Radical Functions 101\" width=\"474\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-101.png 474w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-101-300x121.png 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>Question 7.<br \/>\nWhat is the solution of the inequality 2\\(\\sqrt{x+3}\\) \u2212 1 &lt; 3?<br \/>\nA. x &lt; 1<br \/>\nB. \u22123 &lt; x &lt; 1<br \/>\nC. \u22123 \u2264 x &lt; 1<br \/>\nD. x \u2265 \u22123<\/p>\n<p>Question 8.<br \/>\nWhich function does the graph represent? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-102.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 5 Rational Exponents and Radical Functions 102\" width=\"398\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-102.png 398w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-102-300x145.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p>\n<p>Question 9.<br \/>\nYour friend releases a weather balloon 50 feet from you. The balloon rises vertically. When the balloon is at height h, the distance d between you and the balloon is given by d = \\(\\sqrt{2500+h^{2}}\\), where h and d are measured in feet. Find the inverse of the function. What is the height of the balloon when the distance between you and the balloon is 100 feet?<\/p>\n<p>Question 10.<br \/>\nThe graphs of two functions f and g are shown. Are f and g inverse functions? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-5-Rational-Exponents-and-Radical-Functions-103.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 5 Rational Exponents and Radical Functions 103\" width=\"225\" height=\"186\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions PDF Formatted links are enlisted here for free of cost. So, students who are looking for solutions with detailed &amp; step-wise explanations can refer to this Big Ideas math Book Algebra 2 Ch 5 Answer key and verify their answers while practicing &#8230; <a title=\"Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers-chapter-5\/\" aria-label=\"More on Big Ideas Math Algebra 2 Answers Chapter 5 Rational Exponents and Radical Functions\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":89271,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-5-Rational-Exponents-and-Radical-Functions-54.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/40609"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=40609"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/40609\/revisions"}],"predecessor-version":[{"id":90331,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/40609\/revisions\/90331"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89271"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=40609"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=40609"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=40609"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}