Simplify the Radical Expression fourth root of 405x^3y^2

$\sqrt[4]{405 x^{3} y^{2}}$

Step 1

Rewrite $405 x^{3} y^{2}$ as $3^{4} \cdot (5 x^{3} y^{2})$ .

Factor $81$ out of $405$ .

$\sqrt[4]{81 (5) x^{3} y^{2}}$

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

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