Answer
$\dfrac{2x^3y}{\sqrt[]{xyz}}$
Work Step by Step
Rationalizing the numerator of $
\sqrt[]{\dfrac{8x^5y}{2z}}
$ results to
\begin{array}{l}
\sqrt[]{\dfrac{4x^4\cdot2xy}{2z}}
\\\\=
2x^2\sqrt[]{\dfrac{2xy}{2z}}
\\\\=
2x^2\sqrt[]{\dfrac{xy}{z}}
\\\\=
2x^2\sqrt[]{\dfrac{xy}{z}}
\cdot
\sqrt[]{\dfrac{xy}{xy}}
\\\\=
2x^2\sqrt[]{\dfrac{x^2y^2}{xyz}}
\\\\=
\dfrac{2x^2\cdot xy}{\sqrt[]{xyz}}
\\\\=
\dfrac{2x^3y}{\sqrt[]{xyz}}
.\end{array}