Answer
$\dfrac{3y^3\sqrt[]{10}}{5}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\dfrac{\sqrt[]{270y^2}}{5\sqrt[]{3y^{-4}}}
\\\\=
\dfrac{1}{5}\sqrt[]{\dfrac{270y^2}{3y^{-4}}}
\\\\=
\dfrac{1}{5}\sqrt[]{90y^{2-(-4)}}
\\\\=
\dfrac{1}{5}\sqrt[]{90y^{6}}
\\\\=
\dfrac{1}{5}\sqrt[]{9y^{6}\cdot10}
\\\\=
\dfrac{1}{5}\cdot3y^3\sqrt[]{10}
\\\\=
\dfrac{3y^3\sqrt[]{10}}{5}
.\end{array}
