Answer
8
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, $512^{\frac{1}{3}}=\sqrt[3] 512^{1}=\sqrt[3] 512=8$.
We know that $\sqrt[3] 512=8$, because $8^{3}=512$.
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: 14
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