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: 7

Answer

Choice E

Work Step by Step

Using $a^{-x}=\dfrac{1}{a^x}$ or $\dfrac{1}{a^{-x}}=a^x,$ then \begin{array}{l}\require{cancel} x^{-5/2} \\\\= \dfrac{1}{x^{5/2}} .\end{array} Using $x^{m/n}=\sqrt[n]{x^m}=\left(\sqrt[n]{x} \right)^m,$ then \begin{array}{l}\require{cancel} \dfrac{1}{x^{5/2}} \\\\= \dfrac{1}{(\sqrt[2]{x})^5} \\\\= \dfrac{1}{(\sqrt{x})^5} .\end{array} Hence, $\text{ Choice E .}$
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