#### Answer

$\sqrt[12]{xy}$

#### Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
\sqrt[3]{\sqrt[4]{xy}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\left( \sqrt[4]{xy} \right)^{\frac{1}{3}}
\\\\=
\left( xy^{\frac{1}{4}} \right)^{\frac{1}{3}}
\\\\=
\left( xy \right)^{\frac{1}{4}\cdot\frac{1}{3}}
\\\\=
\left( xy \right)^{\frac{1}{12}}
\\\\=
\sqrt[12]{(xy)^1}
\\\\=
\sqrt[12]{xy}
.\end{array}