Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set - Page 433: 30


$-\frac{4\sqrt[3] a}{b^{3}}$

Work Step by Step

The quotient rule holds that $\sqrt[n] (\frac{a}{b})=\frac{\sqrt[n] a}{\sqrt[n] b}$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $\sqrt[n] b$ is nonzero). Therefore, $-\sqrt[3] (\frac{64a}{b^{9}})=-\frac{\sqrt[3] (64a)}{\sqrt[3] (b^{9})}=-\frac{\sqrt[3] 64\times\sqrt[3] a}{\sqrt[3] (b^{9})}=-\frac{4\sqrt[3] a}{b^{3}}$ We know that $\sqrt[3] 64=4$, because $4^{3}=64$. Also, we know that $\sqrt[3] (b^{9})=b^{3}$, because $(b^{3})^{3}=b^{3\times3}=b^{9}$.
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