Answer
$5x^6\sqrt{3x}$
Work Step by Step
Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $
\sqrt{15x^4}\cdot\sqrt{5x^9}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{15x^4(5x^9)}
\\\\=
\sqrt{75x^{13}}
\\\\=
\sqrt{25x^{12}\cdot3x}
\\\\=
\sqrt{(5x^{6})^2\cdot3x}
\\\\=
5x^6\sqrt{3x}
.\end{array}
Note that variables are assumed to have positive real numbers.
