Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Review Exercises: 26

Answer

-4

Work Step by Step

We are given that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=(\sqrt[n] a)^{m}$, if all indicated roots are real numbers. Therefore, $-8^{\frac{2}{3}}=-(8^{\frac{2}{3}})=-(\sqrt[3] 8^{2})=-[(\sqrt[3] 8)^{2}]=-[(2)^{2}]=-[4]=-4$. We know that $\sqrt[3] 8=2$, because $2^{3}=8$.
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