Answer
$x^2y^{2}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
\left( \sqrt[7]{xy}\right)^{14}
,$ is equivalent to
\begin{array}{l}\require{cancel}
(xy)^{14/7}
\\\\=
(xy)^{2}
\\\\=
x^2y^{2}
.\end{array}