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: 29

Answer

$-\frac{z^{2}\sqrt[3] z}{3x}$

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, $-\sqrt[3] (\frac{z^{7}}{27x^{3}})=-\frac{\sqrt[3] (z^{7})}{\sqrt[3] (27x^{3})}=-\frac{\sqrt[3] (z^{6})\times\sqrt[3] z}{\sqrt[3] (27x^{3}}=-\frac{z^{2}\sqrt[3] z}{3x}$ We know that $\sqrt[3] (z^{6})=z^{2}$, because $(z^{2})^{3}=z^{2\times3}=z^{6}$. Also, we know that $\sqrt[3] (27^{3})=3x$, because $(3x)^{3}=(3\times3\times3)\times x^{1+1+1}=27x^{3}$.
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