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

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

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

Factor $81$ out of $405$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

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