Evaluate sixth root of 1/729

$\sqrt[6]{\frac{1}{729}}$

Step 1

Rewrite $\sqrt[6]{\frac{1}{729}}$ as $\frac{\sqrt[6]{1}}{\sqrt[6]{729}}$ .

$\frac{\sqrt[6]{1}}{\sqrt[6]{729}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[6]{729}}$

Step 3

Simplify the denominator.

Rewrite $729$ as $3^{6}$ .

$\frac{1}{\sqrt[6]{3^{6}}}$

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:

$0.\overline{3}$