Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.2 - Rational Exponents - 7.2 Exercises - Page 448: 18



Work Step by Step

As shown on page 445, we know that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=(\sqrt[n] a)^{m}$. Therefore, $(\frac{8}{27})^{\frac{1}{3}}=\sqrt[3] (\frac{8}{27})^{1}=\sqrt[3] (\frac{8}{27})=\frac{2}{3}$. We know that $\sqrt[3] (\frac{8}{27})=\frac{2}{3}$, because $(\frac{2}{3})^{3}=\frac{2\times2\times2}{3\times3\times3}=\frac{8}{27}$.
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