Answer
$y(2x+3)\sqrt[4]{2x^2}$
Work Step by Step
Perform the indicated operations:
$$\begin{align*}
y\sqrt[4]{32x^6}+\sqrt[4]{162x^2y^4}&=y\sqrt[4]{2^5x^6}+\sqrt[4]{2(3^4)x^2y^4}\\
&=2xy\sqrt[4]{2x^2}+3y\sqrt[4]{2x^2}\\
&=(2xy+3y)\sqrt[4]{2x^2}\\
&=y(2x+3)\sqrt[4]{2x^2}.
\end{align*}$$
