Simplify the Radical Expression fourth root of 81x^2

$\sqrt[4]{81 x^{2}}$

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

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

Pull terms out from under the radical.

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

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

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

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

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

Pull terms out from under the radical.

$3 \sqrt{| x |}$