Simplify sixth root of 8x^3y^9

$\sqrt[6]{8 x^{3} y^{9}}$

Step 1

Rewrite $8 x^{3} y^{9}$ as $y^{6} \cdot (8 x^{3} y^{3})$ .

Factor out $y^{6}$ .

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

Move $x^{3}$ .

$\sqrt[6]{8 y^{6} x^{3} y^{3}}$

Reorder $8$ and $y^{6}$ .

$\sqrt[6]{y^{6} \cdot 8 x^{3} y^{3}}$

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$y \sqrt[6]{8 x^{3} y^{3}}$

Step 3

Rewrite $8 x^{3} y^{3}$ as ${(2 x y)}^{3}$ .

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

Step 4

Rewrite $\sqrt[6]{{(2 x y)}^{3}}$ as $\sqrt{\sqrt[3]{{(2 x y)}^{3}}}$ .

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

Step 5

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

$y \sqrt{2 x y}$