Simplify ( fourth root of a^5)÷2 fourth root of a

$\sqrt[4]{a^{5}} \div 2 \sqrt[4]{a}$

Rewrite the division as a fraction.

$\frac{\sqrt[4]{a^{5}}}{2 \sqrt[4]{a}}$

Combine $\sqrt[4]{a^{5}}$ and $\sqrt[4]{a}$ into a single radical.

$\frac{\sqrt[4]{\frac{a^{5}}{a}}}{2}$

Cancel the common factor of $a^{5}$ and $a$ .

Factor $a$ out of $a^{5}$ .

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

Cancel the common factors.

Raise $a$ to the power of $1$ .

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

Factor $a$ out of $a^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $a^{4}$ by $1$ .

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

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

$\frac{a}{2}$