Simplify ( fourth root of 48a^10)/( fourth root of 3a^2)

$\frac{\sqrt[4]{48 a^{10}}}{\sqrt[4]{3 a^{2}}}$

Step 1

Combine $\sqrt[4]{48 a^{10}}$ and $\sqrt[4]{3 a^{2}}$ into a single radical.

$\sqrt[4]{\frac{48 a^{10}}{3 a^{2}}}$

Step 2

Reduce the expression $\frac{48 a^{10}}{3 a^{2}}$ by cancelling the common factors.

Factor $3$ out of $48 a^{10}$ .

$\sqrt[4]{\frac{3 (16 a^{10})}{3 a^{2}}}$

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

$\sqrt[4]{\frac{3 (16 a^{10})}{3 (a^{2})}}$

Cancel the common factor.

$\sqrt[4]{\frac{3 (16 a^{10})}{3 a^{2}}}$

Rewrite the expression.

$\sqrt[4]{\frac{16 a^{10}}{a^{2}}}$

Step 3

Cancel the common factor of $a^{10}$ and $a^{2}$ .

Factor $a^{2}$ out of $16 a^{10}$ .

$\sqrt[4]{\frac{a^{2} (16 a^{8})}{a^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[4]{\frac{a^{2} (16 a^{8})}{a^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt[4]{\frac{a^{2} (16 a^{8})}{a^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt[4]{\frac{16 a^{8}}{1}}$

Divide $16 a^{8}$ by $1$ .

$\sqrt[4]{16 a^{8}}$

Step 4

Rewrite $16 a^{8}$ as ${(2 a^{2})}^{4}$ .

$\sqrt[4]{{(2 a^{2})}^{4}}$

Step 5

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

$2 a^{2}$