Simplify the Radical Expression 12 root of 4a^2b^4c^2

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

Step 1

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

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

Step 2

Rewrite $\sqrt[12]{{(2 a b^{2} c)}^{2}}$ as $\sqrt[6]{\sqrt{{(2 a b^{2} c)}^{2}}}$ .

$\sqrt[6]{\sqrt{{(2 a b^{2} c)}^{2}}}$

Step 3

Pull terms out from under the radical.

$\sqrt[6]{| 2 a b^{2} c |}$

Step 4

Remove non-negative terms from the absolute value.

$\sqrt[6]{2 b^{2} | a c |}$