Answer
$20x^2y^3\sqrt{y}
$
Work Step by Step
Extracting the factors that are perfect powers of the index, the given expression is equivalent to
\begin{align*}\require{cancel}
&
=5\sqrt{y^6\cdot2x}\cdot2\sqrt{x^2\cdot2xy}
\\\\&=
5\sqrt{(y^3)^2\cdot2x}\cdot2\sqrt{(x)^2\cdot2xy}
\\\\&=
5y^3\sqrt{2x}\cdot2x\sqrt{2xy}
.\end{align*}
Using the rule $a\sqrt{x}\cdot b\sqrt{y}=ab\sqrt{xy},$ the expression above is equivalent to
\begin{align*}
&
=5y^3(2x)\sqrt{2x(2xy)}
\\\\&=
10xy^3\sqrt{4x^2y}
.\end{align*}
Extracting the factors that are perfect powers of the index, the expression above is equivalent to
\begin{align*}\require{cancel}
&
10xy^3\sqrt{(2x)^2\cdot y}
\\\\&=
10xy^3(2x)\sqrt{y}
\\\\&=
20x^2y^3\sqrt{y}
.\end{align*}
Hence, the simplified form of the given expression is $
20x^2y^3\sqrt{y}
$.
