College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Summary, Review, and Test - Review Exercises: 67

Answer

16

Work Step by Step

Based on the definition of $a^{\frac{m}{n}}$, we know that $a^{\frac{m}{n}}=(\sqrt[n] a)^{m}=\sqrt[n] a^{m}$ (where $\sqrt[n] a$ is a real number). Therefore, $64^{\frac{2}{3}}=\sqrt[3] 64^{2}=(\sqrt[3] 64)^{2}=(4)^{2}=16$ We know that $\sqrt[3] 64=4$, because $4^{3}=64$.
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