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 - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set: 65

Answer

$\sqrt[6]{\dfrac{243c^5}{32a^5b^5}}$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{2ab}{3c} \right)^{-5/6} ,$ is equivalent to \begin{array}{l}\require{cancel} \left( \dfrac{3c}{2ab} \right)^{5/6} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $ \left( \dfrac{3c}{2ab} \right)^{5/6} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[6]{\left( \dfrac{3c}{2ab} \right)^{5}} \\\\= \sqrt[6]{\dfrac{3^5c^5}{2^5a^5b^5}} \\\\= \sqrt[6]{\dfrac{243c^5}{32a^5b^5}} .\end{array}
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