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: 31



Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $ (81x)^{3/4} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[4]{(81x)^3} \\\\= \left( \sqrt[4]{81x} \right)^3 \\\\= \left( \sqrt[4]{(3)^4\cdot x} \right)^3 \\\\= \left( 3\sqrt[4]{x} \right)^3 \\\\= 3^3\sqrt[4]{x^3} \\\\= 27\sqrt[4]{x^3} .\end{array}
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