Simplify fourth root of a^2b^14

$\sqrt[4]{a^{2} b^{14}}$

Step 1

Rewrite $a^{2} b^{14}$ as ${(b^{3})}^{4} (a^{2} b^{2})$ .

Factor out $b^{12}$ .

$\sqrt[4]{a^{2} (b^{12} b^{2})}$

Rewrite $b^{12}$ as ${(b^{3})}^{4}$ .

$\sqrt[4]{a^{2} ({(b^{3})}^{4} b^{2})}$

Reorder $a^{2}$ and ${(b^{3})}^{4}$ .

$\sqrt[4]{{(b^{3})}^{4} a^{2} b^{2}}$

Add parentheses.

$\sqrt[4]{{(b^{3})}^{4} (a^{2} b^{2})}$

Step 2

Pull terms out from under the radical.

$b^{3} \sqrt[4]{a^{2} b^{2}}$

Step 3

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

$b^{3} \sqrt[4]{{(a b)}^{2}}$

Step 4

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

$b^{3} \sqrt{\sqrt{{(a b)}^{2}}}$

Step 5

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

$b^{3} \sqrt{a b}$