College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.6 - Rational Exponents - R.6 Exercises - Page 56: 54

Answer

$\text{The given expression simplifies to }\dfrac{1}{16}$.

Work Step by Step

$\begin{array}{ l c } =\dfrac{1}{( -32)^{\dfrac{4}{5}}} & \begin{array}{l} \mathrm{Apply\ the\ rule\ }\\ a^{-b} =\dfrac{1}{a^{b}} \end{array}\\ & \\ =\dfrac{1}{\left(( -32)^{\dfrac{1}{5}}\right)^{4}} & \begin{array}{l} \mathrm{Apply\ the\ rule}\\ a^{n\cdot m} =\left( a^{n}\right)^{m}\\ \end{array}\\ & \\ =\dfrac{1}{\left(\sqrt[5]{-32}\right)^{4}} & \begin{array}{l} \mathrm{Apply\ the\ rule}\\ a^{\frac{b}{c}} =\sqrt[c]{a^{b}} \end{array}\\ & \\ =\dfrac{1}{( -2)^{4}} & \mathrm{Simplify}\\ & \\ =\dfrac{1}{16} & \end{array}$
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