Intermediate Algebra (6th Edition)

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

Chapter 7 - Section 7.1 - Radicals and Radical Functions - Exercise Set: 73

Answer

$-\frac{z^{7}}{3x}$

Work Step by Step

$\sqrt[3] (\frac{z^{21}}{27x^{3}})=\frac{z^{7}}{3x}$, because $(\frac{z^{7}}{3x})^{3}=\frac{z^{7}}{3x}\times\frac{z^{7}}{3x}\times \frac{z^{7}}{3x}=\frac{z^{7+7+7}}{(3\times3\times3)\times x^{1+1+1}}=\frac{z^{21}}{27x^{3}}$ Therefore, $-\sqrt[3] (\frac{z^{21}}{27x^{3}})=-\frac{z^{7}}{3x}$. We are just taking the opposite of $\sqrt[3] (\frac{z^{21}}{27x^{3}})$
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