Evaluate fourth root of 16/81

$\sqrt[4]{\frac{16}{81}}$

Step 1

Rewrite $\sqrt[4]{\frac{16}{81}}$ as $\frac{\sqrt[4]{16}}{\sqrt[4]{81}}$ .

$\frac{\sqrt[4]{16}}{\sqrt[4]{81}}$

Step 2

Simplify the numerator.

Rewrite $16$ as $2^{4}$ .

$\frac{\sqrt[4]{2^{4}}}{\sqrt[4]{81}}$

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

$\frac{2}{\sqrt[4]{81}}$

Step 3

Simplify the denominator.

Rewrite $81$ as $3^{4}$ .

$\frac{2}{\sqrt[4]{3^{4}}}$

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

$\frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$