Answer
$\dfrac{x^2y^2\sqrt[3]{15yz}}{z}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the denominator of the given expression, $
\sqrt[3]{\dfrac{15x^6y^7}{z^2}}
,$ multiply by an expression equal to $1$ which will make the denominator a perfect power of the index. Then extract the root of the factor that is a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying the given expression by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\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}}
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\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}
