Answer
$10x^{6}\sqrt{2x}$
Work Step by Step
Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $
\sqrt{50x^9}\cdot\sqrt{4x^4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{50x^9(4x^4)}
\\\\=
\sqrt{200x^{13}}
\\\\=
\sqrt{100x^{12}\cdot2x}
\\\\=
\sqrt{(10x^{6})^2\cdot2x}
\\\\=
10x^{6}\sqrt{2x}
.\end{array}
Note that variables are assumed to have positive real numbers.
