Answer
$\dfrac{\sqrt[3]{3x^2}}{3x}$
Work Step by Step
Multiplying the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index, the given expression is equivalent to
\begin{align*}\require{cancel}
&
=\dfrac{1}{\sqrt[3]{9x}}\cdot\dfrac{\sqrt[3]{3x^2}}{\sqrt[3]{3x^2}}
\\\\&=
\dfrac{\sqrt[3]{3x^2}}{\sqrt[3]{27x^3}}
\\\\&=
\dfrac{\sqrt[3]{3x^2}}{\sqrt[3]{(3x)^3}}
\\\\&=
\dfrac{\sqrt[3]{3x^2}}{3x}
.\end{align*}
Hence, the simplified form of the given expression is $
\dfrac{\sqrt[3]{3x^2}}{3x}
$.
