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: 25

Answer

27

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, $81^{\frac{3}{4}}=\sqrt[4] 81^{3}=(\sqrt[4] 81)^{3}=3^{3}=27$. We know that $\sqrt[4] 81=3$, because $3^{4}=81$.
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