Answer
$\dfrac{1}{9xy^2}$
Work Step by Step
The expression $
\dfrac{\dfrac{2x}{27y^2}}{\dfrac{6x^2}{9}}
$ simplifies to
\begin{array}{l}
\dfrac{2x}{27y^2}\div\dfrac{6x^2}{9}
\\\\=
\dfrac{2x}{27y^2}\cdot\dfrac{9}{6x^2}
\\\\=
\dfrac{18x}{162x^2y^2}
\\\\=
\dfrac{18x}{18x\cdot9xy^2}
\\\\=
\dfrac{1}{9xy^2}
.\end{array}
