Evaluate fifth root of 32/243

$\sqrt[5]{\frac{32}{243}}$

Step 1

Rewrite $\sqrt[5]{\frac{32}{243}}$ as $\frac{\sqrt[5]{32}}{\sqrt[5]{243}}$ .

$\frac{\sqrt[5]{32}}{\sqrt[5]{243}}$

Step 2

Simplify the numerator.

Rewrite $32$ as $2^{5}$ .

$\frac{\sqrt[5]{2^{5}}}{\sqrt[5]{243}}$

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

$\frac{2}{\sqrt[5]{243}}$

Step 3

Simplify the denominator.

Rewrite $243$ as $3^{5}$ .

$\frac{2}{\sqrt[5]{3^{5}}}$

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

$\frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$