Intermediate Algebra (12th Edition)

Published by Pearson

Chapter 7 - Section 7.2 - Rational Exponents - 7.2 Exercises - Page 448: 27

-1024

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, $-16^{\frac{5}{2}}=-(\sqrt[2] 16^{5})=-((\sqrt 16)^{5})=-(4^{5})=-(1024)=-1024$. We know that $\sqrt 16=4$, because $4^{2}=16$.

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