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: 66

Answer

21

Work Step by Step

The quotient rule holds that $\frac{\sqrt[n] a}{\sqrt[n] b}=\sqrt[n] (\frac{a}{b})$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $\sqrt[n] b$ is nonzero). Therefore, $\frac{7\sqrt[4] 162}{\sqrt[4] 2}=7\sqrt[4] (\frac{162}{2})=7\sqrt[4] 81=7\times3=21$ We know that $\sqrt[4] 81=3$, because $3^{4}=81$
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