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 - Page 641: 32



Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $ (125a)^{2/3} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{(125a)^2} \\\\= \left( \sqrt[3]{125a} \right)^2 \\\\= \left( \sqrt[3]{(5)^3a} \right)^2 \\\\= \left( 5\sqrt[3]{a} \right)^2 \\\\= 5^2\sqrt[3]{a^2} \\\\= 25\sqrt[3]{a^2} .\end{array}
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