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: 26

Answer

36

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, $216^{\frac{2}{3}}=\sqrt[3] 216^{2}=(\sqrt[3] 216)^{2}=6^{2}=36$. We know that $\sqrt[3] 216=6$, because $6^{3}=216$.
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