Simplify cube root of 108^5a^9b^6

$\sqrt[3]{108^{5} a^{9} b^{6}}$

Step 1

Raise $108$ to the power of $5$ .

$\sqrt[3]{14693280768 a^{9} b^{6}}$

Step 2

Rewrite $14693280768 a^{9} b^{6}$ as ${(1944 a^{3} b^{2})}^{3} \cdot 2$ .

Factor $7346640384$ out of $14693280768$ .

$\sqrt[3]{7346640384 (2) a^{9} b^{6}}$

Rewrite $7346640384$ as $1944^{3}$ .

$\sqrt[3]{1944^{3} \cdot 2 a^{9} b^{6}}$

Rewrite $a^{9}$ as ${(a^{3})}^{3}$ .

$\sqrt[3]{1944^{3} \cdot 2 {(a^{3})}^{3} b^{6}}$

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

$\sqrt[3]{1944^{3} \cdot 2 {(a^{3})}^{3} {(b^{2})}^{3}}$

Move $2$ .

$\sqrt[3]{1944^{3} {(a^{3})}^{3} {(b^{2})}^{3} \cdot 2}$

Rewrite $1944^{3} {(a^{3})}^{3} {(b^{2})}^{3}$ as ${(1944 a^{3} b^{2})}^{3}$ .

$\sqrt[3]{{(1944 a^{3} b^{2})}^{3} \cdot 2}$

Step 3

Pull terms out from under the radical.

$1944 a^{3} b^{2} \sqrt[3]{2}$