Simplify the Radical Expression ( fifth root of 96a^7)/( fifth root of 3a^2)

$\frac{\sqrt[5]{96 a^{7}}}{\sqrt[5]{3 a^{2}}}$

Combine $\sqrt[5]{96 a^{7}}$ and $\sqrt[5]{3 a^{2}}$ into a single radical.

$\sqrt[5]{\frac{96 a^{7}}{3 a^{2}}}$

Reduce the expression $\frac{96 a^{7}}{3 a^{2}}$ by cancelling the common factors.

Factor $3$ out of $96 a^{7}$ .

$\sqrt[5]{\frac{3 (32 a^{7})}{3 a^{2}}}$

Factor $3$ out of $3 a^{2}$ .

$\sqrt[5]{\frac{3 (32 a^{7})}{3 (a^{2})}}$

Cancel the common factor.

$\sqrt[5]{\frac{3 (32 a^{7})}{3 a^{2}}}$

Rewrite the expression.

$\sqrt[5]{\frac{32 a^{7}}{a^{2}}}$

Cancel the common factor of $a^{7}$ and $a^{2}$ .

Factor $a^{2}$ out of $32 a^{7}$ .

$\sqrt[5]{\frac{a^{2} (32 a^{5})}{a^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[5]{\frac{a^{2} (32 a^{5})}{a^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt[5]{\frac{a^{2} (32 a^{5})}{a^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt[5]{\frac{32 a^{5}}{1}}$

Divide $32 a^{5}$ by $1$ .

$\sqrt[5]{32 a^{5}}$

Rewrite $32 a^{5}$ as ${(2 a)}^{5}$ .

$\sqrt[5]{{(2 a)}^{5}}$

Pull terms out from under the radical.

$2 a$