Evaluate eighth root of 36a^12b^6

$\sqrt[8]{36 a^{12} b^{6}}$

Step 1

Rewrite $36 a^{12} b^{6}$ as $a^{8} \cdot (36 a^{4} b^{6})$ .

Factor out $a^{8}$ .

$\sqrt[8]{36 (a^{8} a^{4}) b^{6}}$

Reorder $36$ and $a^{8}$ .

$\sqrt[8]{a^{8} \cdot 36 a^{4} b^{6}}$

Add parentheses.

$\sqrt[8]{a^{8} \cdot 36 (a^{4} b^{6})}$

Add parentheses.

$\sqrt[8]{a^{8} \cdot (36 a^{4} b^{6})}$

Step 2

Pull terms out from under the radical.

$a \sqrt[8]{36 a^{4} b^{6}}$

Step 3

Rewrite $36 a^{4} b^{6}$ as ${(6 a^{2} b^{3})}^{2}$ .

$a \sqrt[8]{{(6 a^{2} b^{3})}^{2}}$

Step 4

Rewrite $\sqrt[8]{{(6 a^{2} b^{3})}^{2}}$ as $\sqrt[4]{\sqrt{{(6 a^{2} b^{3})}^{2}}}$ .

$a \sqrt[4]{\sqrt{{(6 a^{2} b^{3})}^{2}}}$

Step 5

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

$a \sqrt[4]{6 a^{2} b^{3}}$