Answer
$\dfrac{y\sqrt[3]{y^2}}{3x^2}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[3]{\dfrac{y^5}{27x^6}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{\dfrac{y^3}{27x^6}\cdot y^2}
\\\\=
\sqrt[3]{\left( \dfrac{y}{3x^2} \right)^3\cdot y^2}
\\\\=
\dfrac{y}{3x^2}\sqrt[3]{y^2}
\\\\=
\dfrac{y\sqrt[3]{y^2}}{3x^2}
.\end{array}