Evaluate cube root of 1/125

$\sqrt[3]{\frac{1}{125}}$

Step 1

Rewrite $\sqrt[3]{\frac{1}{125}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{125}}$ .

$\frac{\sqrt[3]{1}}{\sqrt[3]{125}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[3]{125}}$

Step 3

Simplify the denominator.

Rewrite $125$ as $5^{3}$ .

$\frac{1}{\sqrt[3]{5^{3}}}$

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

$\frac{1}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$