## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 7 - Section 7.2 - Rational Exponents - 7.2 Exercises: 29

16

#### Work Step by Step

As shown on page 445, we know that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=(\sqrt[n] a)^{m}$. Therefore, $(-8)^{\frac{4}{3}}=\sqrt[3] (-8)^{4}=(\sqrt[3] -8)^{4}=(-2)^{4}=16$. We know that $\sqrt[3] -8=-2$, because $(-2)^{3}=-8$.

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