Simplify fourth root of 128x^7y^7

$\sqrt[4]{128 x^{7} y^{7}}$

Step 1

Rewrite $128 x^{7} y^{7}$ as ${(2 x y)}^{4} \cdot (8 x^{3} y^{3})$ .

Factor $16$ out of $128$ .

$\sqrt[4]{16 (8) x^{7} y^{7}}$

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} \cdot 8 x^{7} y^{7}}$

Factor out $x^{4}$ .

$\sqrt[4]{2^{4} \cdot 8 (x^{4} x^{3}) y^{7}}$

Factor out $y^{4}$ .

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

Move $x^{3}$ .

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

Move $8$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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