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: 57

Answer

$8$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{1}{16} \right)^{-3/4} ,$ is equivalent to \begin{array}{l}\require{cancel} 16^{3/4} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $ 16^{3/4} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[4]{16^3} \\\\= \left( \sqrt[4]{16} \right) ^3 \\\\= \left( \sqrt[4]{(2)^4} \right) ^3 \\\\= \left( 2 \right) ^3 \\\\= 8 .\end{array}
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