Answer
$\dfrac{4x^2\sqrt[3]{x}}{6y^2}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[3]{\dfrac{64x^7}{216y^6}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3]{64x^7}}{\sqrt[3]{216y^6}}
\\\\=
\dfrac{\sqrt[3]{64x^6\cdot x}}{\sqrt[3]{216y^6}}
\\\\=
\dfrac{\sqrt[3]{(4x^2)^3\cdot x}}{\sqrt[3]{(6y^2)^3}}
\\\\=
\dfrac{4x^2\sqrt[3]{x}}{6y^2}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.