College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Summary, Review, and Test - Review Exercises: 66

Answer

$\frac{1}{3}$

Work Step by Step

We know that $b^{-n}=\frac{1}{b^{n}}$ (where $b$ is a nonzero real number and $n$ is a natural number). Therefore, $27^{-\frac{1}{3}}=\frac{1}{27^{\frac{1}{3}}}$ Based on the definition of $a^{\frac{m}{n}}$, we know that $a^{\frac{m}{n}}=(\sqrt[n] a)^{m}=\sqrt[n] a^{m}$ (where $\sqrt[n] a$ is a real number). Therefore, $\frac{1}{27^{\frac{1}{3}}}=\frac{1}{\sqrt[3] 27^{1}}=\frac{1}{\sqrt[3] 27}=\frac{1}{3}$ We know that $\sqrt[3] 27=3$, because $3^{3}=27$.
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