Simplify ( fourth root of a^8b^10)/( fourth root of b^6)

$\frac{\sqrt[4]{a^{8} b^{10}}}{\sqrt[4]{b^{6}}}$

Step 1

Combine $\sqrt[4]{a^{8} b^{10}}$ and $\sqrt[4]{b^{6}}$ into a single radical.

$\sqrt[4]{\frac{a^{8} b^{10}}{b^{6}}}$

Step 2

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{a^{8} b^{10}}{b^{6}}$ by cancelling the common factors.

Factor $b^{6}$ out of $a^{8} b^{10}$ .

$\sqrt[4]{\frac{b^{6} (a^{8} b^{4})}{b^{6}}}$

Multiply by $1$ .

$\sqrt[4]{\frac{b^{6} (a^{8} b^{4})}{b^{6} \cdot 1}}$

Cancel the common factor.

$\sqrt[4]{\frac{b^{6} (a^{8} b^{4})}{b^{6} \cdot 1}}$

Rewrite the expression.

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

Divide $a^{8} b^{4}$ by $1$ .

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

Step 3

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

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

Step 4

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

$a^{2} b$