Simplify the Radical Expression fourth root of a^2b^14

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

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.

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

Pull terms out from under the radical.

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

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

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

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

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

Pull terms out from under the radical.

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