Answer
$\dfrac{x^2y^2\sqrt[3]{15yz}}{z}$
Work Step by Step
Multiplying both the numerator and the denominator by a factor that will make the denominator a perfect power of the radical, the rationalized-denominator form of the given expression, $
\sqrt[3]{\dfrac{15x^6y^7}{z^2}}
,$ is
\begin{array}{l}\require{cancel}
\sqrt[3]{\dfrac{15x^6y^7}{z^2}\cdot\dfrac{z}{z}}
\\\\=
\sqrt[3]{\dfrac{15x^6y^7z}{z^3}}
\\\\=
\sqrt[3]{\dfrac{x^6y^6}{z^3}\cdot15yz}
\\\\=
\sqrt[3]{\left( \dfrac{x^2y^2}{z} \right)^3\cdot15yz}
\\\\=
\dfrac{x^2y^2}{z}\sqrt[3]{15yz}
\\\\=
\dfrac{x^2y^2\sqrt[3]{15yz}}{z}
.\end{array}
Note that all variables are assumed to have positive real numbers.