Simplify the Radical Expression eighth root of 49a^8b^2

$\sqrt[8]{49 a^{8} b^{2}}$

Rewrite $49 a^{8} b^{2}$ as $a^{8} \cdot (49 b^{2})$ .

Reorder $49$ and $a^{8}$ .

$\sqrt[8]{a^{8} \cdot 49 b^{2}}$

Add parentheses.

$\sqrt[8]{a^{8} \cdot (49 b^{2})}$

Pull terms out from under the radical.

$| a | \sqrt[8]{49 b^{2}}$

Rewrite $49 b^{2}$ as ${(7 b)}^{2}$ .

$| a | \sqrt[8]{{(7 b)}^{2}}$

Rewrite $\sqrt[8]{{(7 b)}^{2}}$ as $\sqrt[4]{\sqrt{{(7 b)}^{2}}}$ .

$| a | \sqrt[4]{\sqrt{{(7 b)}^{2}}}$

Pull terms out from under the radical.

$| a | \sqrt[4]{| 7 b |}$

Remove non-negative terms from the absolute value.

$| a | \sqrt[4]{7 | b |}$