Simplify fourth root of 4x^3y^2* fourth root of 4xy^2

$\sqrt[4]{4 x^{3} y^{2}} \cdot \sqrt[4]{4 x y^{2}}$

Multiply $\sqrt[4]{4 x^{3} y^{2}} \sqrt[4]{4 x y^{2}}$ .

Combine using the product rule for radicals.

$\sqrt[4]{4 x^{3} y^{2} (4 x y^{2})}$

Multiply $4$ by $4$ .

$\sqrt[4]{16 x^{3} y^{2} (x y^{2})}$

Raise $x$ to the power of $1$ .

$\sqrt[4]{16 (x^{1} x^{3}) y^{2} y^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[4]{16 x^{1 + 3} y^{2} y^{2}}$

Add $1$ and $3$ .

$\sqrt[4]{16 x^{4} y^{2} y^{2}}$

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\sqrt[4]{16 x^{4} (y^{2} y^{2})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[4]{16 x^{4} y^{2 + 2}}$

Add $2$ and $2$ .

$\sqrt[4]{16 x^{4} y^{4}}$

Rewrite $16 x^{4} y^{4}$ as ${(2 x y)}^{4}$ .

$\sqrt[4]{{(2 x y)}^{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$2 x y$