Simplify 2 fourth root of 8x^3y^2*3 fourth root of 2x^5y^2

$2 \sqrt[4]{8 x^{3} y^{2}} \cdot 3 \sqrt[4]{2 x^{5} y^{2}}$

Rewrite $2 x^{5} y^{2}$ as $x^{4} \cdot (2 x y^{2})$ .

Factor out $x^{4}$ .

$2 \sqrt[4]{8 x^{3} y^{2}} \cdot (3 \sqrt[4]{2 (x^{4} x) y^{2}})$

Reorder $2$ and $x^{4}$ .

$2 \sqrt[4]{8 x^{3} y^{2}} \cdot (3 \sqrt[4]{x^{4} \cdot 2 x y^{2}})$

Add parentheses.

$2 \sqrt[4]{8 x^{3} y^{2}} \cdot (3 \sqrt[4]{x^{4} \cdot 2 (x y^{2})})$

Add parentheses.

$2 \sqrt[4]{8 x^{3} y^{2}} \cdot (3 \sqrt[4]{x^{4} \cdot (2 x y^{2})})$

Pull terms out from under the radical.

$2 \sqrt[4]{8 x^{3} y^{2}} \cdot (3 (x \sqrt[4]{2 x y^{2}}))$

Multiply $2 \sqrt[4]{8 x^{3} y^{2}} (3 x \sqrt[4]{2 x y^{2}})$ .

Multiply $3$ by $2$ .

$6 \sqrt[4]{8 x^{3} y^{2}} (x \sqrt[4]{2 x y^{2}})$

Combine using the product rule for radicals.

$6 (x \sqrt[4]{8 x^{3} y^{2} (2 x y^{2})})$

Multiply $2$ by $8$ .

$6 (x \sqrt[4]{16 x^{3} y^{2} (x y^{2})})$

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

$6 (x \sqrt[4]{16 (x^{1} x^{3}) y^{2} y^{2}})$

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

$6 (x \sqrt[4]{16 x^{1 + 3} y^{2} y^{2}})$

Add $1$ and $3$ .

$6 (x \sqrt[4]{16 x^{4} y^{2} y^{2}})$

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

Move $y^{2}$ .

$6 (x \sqrt[4]{16 x^{4} (y^{2} y^{2})})$

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

$6 (x \sqrt[4]{16 x^{4} y^{2 + 2}})$

Add $2$ and $2$ .

$6 (x \sqrt[4]{16 x^{4} y^{4}})$

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

$6 (x \sqrt[4]{{(2 x y)}^{4}})$

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

$6 (x (2 x y))$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$6 (x \cdot x (2 y))$

Multiply $x$ by $x$ .

$6 (x^{2} (2 y))$

Rewrite using the commutative property of multiplication.

$6 (2 x^{2} y)$

Multiply $2$ by $6$ .

$12 x^{2} y$