Answer
The fill in the blank is $\frac{5}{3}$.
Work Step by Step
The given expression is
$\sqrt[3] {2^5}$
The index $3$ is the exponent's denominator, and the power $5$ is the numerator.
We can write
$2^{\frac{5}{3}}$.
Intermediate Algebra for College Students (7th Edition)
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13417-894-7
ISBN 13:
978-0-13417-894-3
Chapter 7 - Section 7.2 - Rational Exponents - Concept and Vocabulary Check - Page 521: 6
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