Answer
$-\dfrac{\sqrt[3]{6xy}}{y}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
-\sqrt[3]{\dfrac{6x}{y^2}}
,$ multiply the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying the numerator and the denominator 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{6x}{y^2}\cdot\dfrac{y}{y}}
\\\\=
-\sqrt[3]{\dfrac{6xy}{y^3}}
.\end{array}
Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
-\dfrac{\sqrt[3]{6xy}}{\sqrt[3]{y^3}}
\\\\=
-\dfrac{\sqrt[3]{6xy}}{y}
.\end{array}
