Answer
$243$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
9^{5/2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[]{9^5}
\\\\=
\left( \sqrt[]{9} \right)^5
\\\\=
\left( \sqrt[]{(3)^2} \right)^5
\\\\=
\left( 3 \right)^5
\\\\=
243
.\end{array}