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: 61

Answer

$\dfrac{2\sqrt[4]{a^3}\sqrt[3]{c^2}}{\sqrt{b}}$

Work Step by Step

Using the laws of exponents, the given expression, $ 2a^{3/4}b^{-1/2}c^{2/3} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{2a^{3/4}c^{2/3}}{b^{1/2}} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $ \dfrac{2a^{3/4}c^{2/3}}{b^{1/2}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{2\sqrt[4]{a^3}\sqrt[3]{c^2}}{\sqrt{b}} .\end{array}
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