Answer
$\dfrac{2x}{y}\sqrt[5]{\dfrac{x^2}{y}}$
Work Step by Step
Using the properties of radicals, the expression $
\dfrac{\sqrt[5]{64x^{9}y^{2}}}{\sqrt[5]{2x^2y^{-8}}}
$ simplifies to
\begin{array}{l}
\sqrt[5]{\dfrac{64x^{9}y^{2}}{2x^2y^{-8}}}
\\\\=
\sqrt[5]{32x^{9-2}y^{2-(8)}}
\\\\=
\sqrt[5]{32x^{7}y^{-6}}
\\\\=
\sqrt[5]{\dfrac{32x^{7}}{y^{6}}}
\\\\=
\sqrt[5]{\dfrac{32x^{5}}{y^{5}}\cdot \dfrac{x^2}{y}}
\\\\=
\dfrac{2x}{y}\sqrt[5]{\dfrac{x^2}{y}}
.\end{array}
