Answer
$a)$ $x^{2}y^{2}$
$b)$ $xy^{2}$
Work Step by Step
$a)$ $\sqrt[3]{(x^{3}y)^{2}y^{4}}$
Evaluate the power inside the root:
$\sqrt[3]{(x^{3}y)^{2}y^{4}}=\sqrt[3]{(x^{6}y^{2})y^{4}}=...$
Evaluate the product inside the root:
$...=\sqrt[3]{x^{6}y^{2+4}}=\sqrt[3]{x^{6}y^{6}}=...$
Evaluate the root:
$...=x^{2}y^{2}$
$b)$ $\sqrt{x^{2}y^{4}}$
Evaluate the square root:
$\sqrt{x^{2}y^{4}}=xy^{2}$
