Answer
$2xy$
Work Step by Step
Extracting the factors that are perfect powers of the index, the given expression, $
\sqrt{\sqrt{16x^4y^4}}
,$ is equivalent to
\begin{align*}\require{cancel}
&
\sqrt{\sqrt{(4x^2y^2)^2}}
\\\\&=
\sqrt{4x^2y^2}
\\\\&=
\sqrt{(2xy)^2}
\\\\&=
2xy
.\end{align*}
Hence, the given expression simplifies to $
2xy
$.
