Simplify ( fourth root of 2^4)/( fourth root of 2^8)

$\frac{\sqrt[4]{2^{4}}}{\sqrt[4]{2^{8}}}$

Combine $\sqrt[4]{2^{4}}$ and $\sqrt[4]{2^{8}}$ into a single radical.

$\sqrt[4]{\frac{2^{4}}{2^{8}}}$

Reduce the expression $\frac{2^{4}}{2^{8}}$ by cancelling the common factors.

Multiply by $1$ .

$\sqrt[4]{\frac{2^{4} \cdot 1}{2^{8}}}$

Factor $2^{4}$ out of $2^{8}$ .

$\sqrt[4]{\frac{2^{4} \cdot 1}{2^{4} \cdot 2^{4}}}$

Cancel the common factor.

$\sqrt[4]{\frac{2^{4} \cdot 1}{2^{4} \cdot 2^{4}}}$

Rewrite the expression.

$\sqrt[4]{\frac{1}{2^{4}}}$

Raise $2$ to the power of $4$ .

$\sqrt[4]{\frac{1}{16}}$

Rewrite $\sqrt[4]{\frac{1}{16}}$ as $\frac{\sqrt[4]{1}}{\sqrt[4]{16}}$ .

$\frac{\sqrt[4]{1}}{\sqrt[4]{16}}$

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[4]{16}}$

Simplify the denominator.

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

$\frac{1}{\sqrt[4]{2^{4}}}$

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

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$