Simplify the Radical Expression 12 root of 16x^16y^20

$\sqrt[12]{16 x^{16} y^{20}}$

Step 1

Rewrite $16 x^{16} y^{20}$ as ${(x y)}^{12} \cdot (16 x^{4} y^{8})$ .

Factor out $x^{12}$ .

$\sqrt[12]{16 (x^{12} x^{4}) y^{20}}$

Factor out $y^{12}$ .

$\sqrt[12]{16 (x^{12} x^{4}) (y^{12} y^{8})}$

Move $x^{4}$ .

$\sqrt[12]{16 (x^{12}) y^{12} x^{4} y^{8}}$

Move $16$ .

$\sqrt[12]{(x^{12}) y^{12} \cdot 16 x^{4} y^{8}}$

Rewrite $(x^{12}) y^{12}$ as ${(x y)}^{12}$ .

$\sqrt[12]{{(x y)}^{12} \cdot 16 x^{4} y^{8}}$

Add parentheses.

$\sqrt[12]{{(x y)}^{12} \cdot 16 (x^{4} y^{8})}$

Add parentheses.

$\sqrt[12]{{(x y)}^{12} \cdot (16 x^{4} y^{8})}$

Step 2

Pull terms out from under the radical.

$| x y | \sqrt[12]{16 x^{4} y^{8}}$

Step 3

Rewrite $16 x^{4} y^{8}$ as ${(2 x y^{2})}^{4}$ .

$| x y | \sqrt[12]{{(2 x y^{2})}^{4}}$

Step 4

Rewrite $\sqrt[12]{{(2 x y^{2})}^{4}}$ as $\sqrt[3]{\sqrt[4]{{(2 x y^{2})}^{4}}}$ .

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

Step 5

Pull terms out from under the radical.

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

Step 6

Remove non-negative terms from the absolute value.

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