Answer
$2xy^{2}\sqrt[4]{xy^3}$
Work Step by Step
Extracting the factors that are perfect roots of the given index, the given expression, $
\sqrt[4]{16x^5y^{11}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[4]{16x^4y^{8}\cdot xy^3}
\\\\=
\sqrt[4]{(2xy^{2})^4\cdot xy^3}
\\\\=
2xy^{2}\sqrt[4]{xy^3}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.