Simplify fourth root of 162x^7y^20

$\sqrt[4]{162 x^{7} y^{20}}$

Step 1

Rewrite $162 x^{7} y^{20}$ as ${(3 x y^{5})}^{4} \cdot (2 x^{3})$ .

Factor $81$ out of $162$ .

$\sqrt[4]{81 (2) x^{7} y^{20}}$

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} \cdot 2 x^{7} y^{20}}$

Factor out $x^{4}$ .

$\sqrt[4]{3^{4} \cdot 2 (x^{4} x^{3}) y^{20}}$

Rewrite $y^{20}$ as ${(y^{5})}^{4}$ .

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

Move $x^{3}$ .

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

Move $2$ .

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

Rewrite $(3^{4} (x^{4})) {(y^{5})}^{4}$ as ${(3 x y^{5})}^{4}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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