Answer
$2|y|\sqrt[4]{4x^3y^2}$
Work Step by Step
Extracting the perfect powers of the index, the given expression, $
\sqrt[4]{64x^3y^6}
,$ is equivalent to
\begin{align*}
&
=\sqrt[4]{16y^4\cdot4x^3y^2}
\\\\&=
\sqrt[4]{\left(2y\right)^4\cdot4x^3y^2}
\\\\&=
|2y|\sqrt[4]{4x^3y^2}
\\\\&=
2|y|\sqrt[4]{4x^3y^2}
.\end{align*}
Hence, the simplified form of the given expression is $
2|y|\sqrt[4]{4x^3y^2}
$.
