Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set - Page 424: 32

Answer

$\dfrac{1}{16}$

Work Step by Step

Using $a^{\frac{m}{n}}=\sqrt[n]{a^m}$ and the laws of exponents, then, \begin{align*} (-8)^{-4/3} \\\\= \dfrac{1}{(-8)^{4/3}} \\\\= \dfrac{1}{(\sqrt[3]{-8})^{4}} \\\\= \dfrac{1}{(-2)^{4}} \\\\= \dfrac{1}{16} .\end{align*}
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