Evaluate fourth root of 81/625

$\sqrt[4]{\frac{81}{625}}$

Step 1

Rewrite $\sqrt[4]{\frac{81}{625}}$ as $\frac{\sqrt[4]{81}}{\sqrt[4]{625}}$ .

$\frac{\sqrt[4]{81}}{\sqrt[4]{625}}$

Step 2

Simplify the numerator.

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

$\frac{\sqrt[4]{3^{4}}}{\sqrt[4]{625}}$

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

$\frac{3}{\sqrt[4]{625}}$

Step 3

Simplify the denominator.

Rewrite $625$ as $5^{4}$ .

$\frac{3}{\sqrt[4]{5^{4}}}$

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

$\frac{3}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{5}$

Decimal Form:

$0.6$