Answer
512
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, $64^{\frac{3}{2}}=\sqrt[2] (64)^{3}=(\sqrt 64)^{3}=8^{3}=512$.
We know that $\sqrt 64=8$, because $8^{2}=64$.
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: 24
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