Answer
$3x^{2}y^{2}\sqrt[4]{xy^3}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[4]{9x^7y^2}\sqrt[4]{9x^2y^9}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[4]{9x^7y^2(9x^2y^9)}
\\\\=
\sqrt[4]{81x^{7+2}y^{2+9}}
\\\\=
\sqrt[4]{81x^{9}y^{11}}
\\\\=
\sqrt[4]{81x^{8}y^{8}\cdot xy^3}
\\\\=
\sqrt[4]{(3x^{2}y^{2})^4\cdot xy^3}
\\\\=
3x^{2}y^{2}\sqrt[4]{xy^3}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.