Answer
$\dfrac{5x\sqrt[3]{2x}}{8}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{1}{8}\sqrt[3]{250x^4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{8}\sqrt[3]{125x^3\cdot2x}
\\\\=
\dfrac{1}{8}\sqrt[3]{(5x)^3\cdot2x}
\\\\=
\dfrac{1}{8}\cdot5x\sqrt[3]{2x}
\\\\=
\dfrac{5x}{8}\sqrt[3]{2x}
\\\\=
\dfrac{5x\sqrt[3]{2x}}{8}
.\end{array}
Note that all of the variables are assumed to represent non-negative real numbers.