Simplify the Radical Expression fourth root of 16/81

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

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

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

Simplify the numerator.

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

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

Pull terms out from under the radical.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Simplify the denominator.

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

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

Pull terms out from under the radical.

$\frac{2}{| 3 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\frac{2}{3}$