Algebra Examples

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

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.

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Step 3.1

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

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

Step 3.2

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

$\frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$