Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises: 95

Answer

$-3r^{3}s^{2}\sqrt[4]{2r^3s^2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ -\sqrt[4]{162r^{15}s^{10}} ,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers. $\bf{\text{Solution Details:}}$ Expressing the radicand of the expression above with a factor that is a perfect power of the index and then extracting the root of that factor results to \begin{array}{l}\require{cancel} -\sqrt[4]{81r^{12}s^{8}\cdot2r^3s^2} \\\\= -\sqrt[4]{(3r^{3}s^{2})^4\cdot2r^3s^2} \\\\= -3r^{3}s^{2}\sqrt[4]{2r^3s^2} .\end{array}
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