Answer
$125x^{6}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
(25x^4)^{3/2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[]{(25x^4)^3}
\\\\=
\left( \sqrt[]{25x^4} \right)^3
\\\\=
\left( \sqrt[]{(5x^2)^2} \right)^3
\\\\=
\left( 5x^2 \right)^3
\\\\=
5^3x^{2(3)}
\\\\=
125x^{6}
.\end{array}
