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: 33

Answer

$125x^{6}$

Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $ (25x^4)^{3/2} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[]{(25x^4)^3} \\\\= \left( \sqrt[]{25x^4} \right)^3 \\\\= \left( \sqrt[]{(5x^2)^2} \right)^3 \\\\= \left( 5x^2 \right)^3 \\\\= 5^3x^{2(3)} \\\\= 125x^{6} .\end{array}
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