Answer
$x^{}(y+z)^{2}\sqrt[5]{x}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[5]{x^3(y+z)^6}\sqrt[5]{x^3(y+z)^4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[5]{x^3(y+z)^6\cdot x^3(y+z)^4 }
\\\\=
\sqrt[5]{x^{3+3}(y+z)^{6+4}}
\\\\=
\sqrt[5]{x^{6}(y+z)^{10}}
\\\\=
\sqrt[5]{x^{5}(y+z)^{10}\cdot x}
\\\\=
\sqrt[5]{\left[ x^{}(y+z)^{2} \right]^5\cdot x}
\\\\=
x^{}(y+z)^{2}\sqrt[5]{x}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.