Simplify cube root of 1/343

$\sqrt[3]{\frac{1}{343}}$

Step 1

Rewrite $\sqrt[3]{\frac{1}{343}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{343}}$ .

$\frac{\sqrt[3]{1}}{\sqrt[3]{343}}$

Step 2

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[3]{343}}$

Step 3

Simplify the denominator.

Rewrite $343$ as $7^{3}$ .

$\frac{1}{\sqrt[3]{7^{3}}}$

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

$\frac{1}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7}$

Decimal Form:

$0.\overline{142857}$