Evaluate sixth root of 1/15625

$\sqrt[6]{\frac{1}{15625}}$

Step 1

Rewrite $\sqrt[6]{\frac{1}{15625}}$ as $\frac{\sqrt[6]{1}}{\sqrt[6]{15625}}$ .

$\frac{\sqrt[6]{1}}{\sqrt[6]{15625}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[6]{15625}}$

Step 3

Simplify the denominator.

Rewrite $15625$ as $5^{6}$ .

$\frac{1}{\sqrt[6]{5^{6}}}$

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

$\frac{1}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$