Answer
$\dfrac{3\sqrt{xy}}{4y^2}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{3\sqrt{x}}{4\sqrt{y^3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3\sqrt{x}}{4\sqrt{y^2\cdot y}}
\\\\=
\dfrac{3\sqrt{x}}{4\sqrt{(y)^2\cdot y}}
\\\\=
\dfrac{3\sqrt{x}}{4y\sqrt{y}}
\\\\=
\dfrac{3\sqrt{x}}{4y\sqrt{y}}\cdot\dfrac{\sqrt{y}}{\sqrt{y}}
\\\\=
\dfrac{3\sqrt{xy}}{4y\cdot y}
\\\\=
\dfrac{3\sqrt{xy}}{4y^2}
.\end{array}
Note that all variables are assumed to have positive values.
