Simplify the Radical Expression fourth root of 1/81

$\sqrt[4]{\frac{1}{81}}$

Step 1

Rewrite $\sqrt[4]{\frac{1}{81}}$ as $\frac{\sqrt[4]{1}}{\sqrt[4]{81}}$ .

$\frac{\sqrt[4]{1}}{\sqrt[4]{81}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[4]{81}}$

Step 3

Simplify the denominator.

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

$\frac{1}{\sqrt[4]{3^{4}}}$

Pull terms out from under the radical.

$\frac{1}{| 3 |}$

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

$\frac{1}{3}$