Simplify -11ab cube root of a^12b^18

$- 11 a b \sqrt[3]{a^{12} b^{18}}$

Step 1

Rewrite $a^{12} b^{18}$ as ${(a^{4} b^{6})}^{3}$ .

$- 11 a b \sqrt[3]{{(a^{4} b^{6})}^{3}}$

Step 2

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

$- 11 a b (a^{4} b^{6})$

Step 3

Multiply $a$ by $a^{4}$ by adding the exponents.

Move $a^{4}$ .

$- 11 (a^{4} a) b \cdot b^{6}$

Multiply $a^{4}$ by $a$ .

Raise $a$ to the power of $1$ .

$- 11 (a^{4} a^{1}) b \cdot b^{6}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 11 a^{4 + 1} b \cdot b^{6}$

Add $4$ and $1$ .

$- 11 a^{5} b \cdot b^{6}$

Step 4

Multiply $b$ by $b^{6}$ by adding the exponents.

Move $b^{6}$ .

$- 11 a^{5} (b^{6} b)$

Multiply $b^{6}$ by $b$ .

Raise $b$ to the power of $1$ .

$- 11 a^{5} (b^{6} b^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 11 a^{5} b^{6 + 1}$

Add $6$ and $1$ .

$- 11 a^{5} b^{7}$