Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set - Page 653: 10


Choice D

Work Step by Step

Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression, $ \sqrt[3]{\dfrac{a^2}{b^6}} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{a^2}{b^6}} \\\\= \dfrac{\sqrt[3]{a^2}}{\sqrt[3]{b^6}} \\\\= \dfrac{\sqrt[3]{a^2}}{\sqrt[3]{(b^2)^3}} \\\\= \dfrac{\sqrt[3]{a^2}}{b^2} .\end{array} Hence, $\text{ Choice D .}$
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