Evaluate fourth root of 81x^8y^6

$\sqrt[4]{81 x^{8} y^{6}}$

Rewrite $81 x^{8} y^{6}$ as ${(3 x^{2} y)}^{4} y^{2}$ .

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

$\sqrt[4]{3^{4} x^{8} y^{6}}$

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

$\sqrt[4]{3^{4} {(x^{2})}^{4} y^{6}}$

Factor out $y^{4}$ .

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

Rewrite $3^{4} {(x^{2})}^{4} y^{4}$ as ${(3 x^{2} y)}^{4}$ .

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

Pull terms out from under the radical.

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

Rewrite $\sqrt[4]{y^{2}}$ as $\sqrt{\sqrt{y^{2}}}$ .

$3 x^{2} y \sqrt{\sqrt{y^{2}}}$

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

$3 x^{2} y \sqrt{y}$