Simplify sixth root of 448x^7y^7

$\sqrt[6]{448 x^{7} y^{7}}$

Step 1

Rewrite $448 x^{7} y^{7}$ as ${(2 x y)}^{6} \cdot (7 x y)$ .

Factor $64$ out of $448$ .

$\sqrt[6]{64 (7) x^{7} y^{7}}$

Rewrite $64$ as $2^{6}$ .

$\sqrt[6]{2^{6} \cdot 7 x^{7} y^{7}}$

Factor out $x^{6}$ .

$\sqrt[6]{2^{6} \cdot 7 (x^{6} x) y^{7}}$

Factor out $y^{6}$ .

$\sqrt[6]{2^{6} \cdot 7 (x^{6} x) (y^{6} y)}$

Move $x$ .

$\sqrt[6]{2^{6} \cdot 7 (x^{6}) y^{6} x y}$

Move $7$ .

$\sqrt[6]{(2^{6} (x^{6})) y^{6} \cdot 7 x y}$

Rewrite $(2^{6} (x^{6})) y^{6}$ as ${(2 x y)}^{6}$ .

$\sqrt[6]{{(2 x y)}^{6} \cdot 7 x y}$

Add parentheses.

$\sqrt[6]{{(2 x y)}^{6} \cdot 7 (x y)}$

Add parentheses.

$\sqrt[6]{{(2 x y)}^{6} \cdot (7 x y)}$

Step 2

Pull terms out from under the radical.

$2 x y \sqrt[6]{7 x y}$