Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\dfrac{4x^2\sqrt[3]{x}}{6y^2}$
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.