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: 23

Answer

$\sqrt{ab}$

Work Step by Step

Using the laws of exponents and that $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $ (a^2b^2)^{1/4} ,$ is equivalent to \begin{array}{l}\require{cancel} ((ab)^2)^{1/4} \\\\= (ab)^{2\cdot\frac{1}{4}} \\\\= (ab)^{2\cdot\frac{1}{4}} \\\\= (ab)^{\frac{2}{4}} \\\\= (ab)^{\frac{1}{2}} \\\\= \sqrt{(ab)^1} \\\\= \sqrt{ab} .\end{array}
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