Simplify cube root of 1/27

$\sqrt[3]{\frac{1}{27}}$

Step 1

Rewrite $\sqrt[3]{\frac{1}{27}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{27}}$ .

$\frac{\sqrt[3]{1}}{\sqrt[3]{27}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[3]{27}}$

Step 3

Simplify the denominator.

Rewrite $27$ as $3^{3}$ .

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

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

$\frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$