Answer
$\dfrac{27}{16\sqrt 2}$
Work Step by Step
Since $9=3^2$ and $8=2(2^2)$, we have
$$
\left(\frac{9}{8}\right)^{3/2}=\left(\frac{3^2}{2(2^2)}\right)^{3/2}=\frac{3^3}{2^3\sqrt{2^3}}=\frac{27}{16\sqrt 2}
.$$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Appendix A - Review - A.7 nth Roots; Rational Exponents - A.7 Assess Your Understanding - Page A61: 63
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