Evaluate fourth root of 1/4 fourth root of 1/64

$\sqrt[4]{\frac{1}{4}} \sqrt[4]{\frac{1}{64}}$

Combine using the product rule for radicals.

$\sqrt[4]{\frac{1}{4} \cdot \frac{1}{64}}$

Multiply $\frac{1}{4}$ by $\frac{1}{64}$ .

$\sqrt[4]{\frac{1}{4 \cdot 64}}$

Multiply $4$ by $64$ .

$\sqrt[4]{\frac{1}{256}}$

Rewrite $\sqrt[4]{\frac{1}{256}}$ as $\frac{\sqrt[4]{1}}{\sqrt[4]{256}}$ .

$\frac{\sqrt[4]{1}}{\sqrt[4]{256}}$

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[4]{256}}$

Simplify the denominator.

Rewrite $256$ as $4^{4}$ .

$\frac{1}{\sqrt[4]{4^{4}}}$

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

$\frac{1}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$