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 $3^{4}=81$.
Intermediate Algebra (12th Edition)
by Lial, Margaret L.; Hornsby, John; McGinnis, Terry
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: 25
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