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