Intermediate Algebra (12th Edition)

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

Chapter 7 - Section 7.2 - Rational Exponents - 7.2 Exercises: 17

Answer

$\frac{8}{9}$

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, $(\frac{64}{81})^{\frac{1}{2}}=\sqrt[2] (\frac{64}{81})^{1}=\sqrt (\frac{64}{81})=\frac{8}{9}$. We know that $\sqrt (\frac{64}{81})=\frac{8}{9}$, because $(\frac{8}{9})^{2}=(\frac{64}{81})$.
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