Simplify -12a^4b^2*3ab^3c^2

$- 12 a^{4} b^{2} \cdot 3 a b^{3} c^{2}$

Step 1

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

Move $a$ .

$- 12 (a \cdot a^{4}) b^{2} \cdot (3 b^{3} c^{2})$

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

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

$- 12 (a^{1} a^{4}) b^{2} \cdot (3 b^{3} c^{2})$

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

$- 12 a^{1 + 4} b^{2} \cdot (3 b^{3} c^{2})$

Add $1$ and $4$ .

$- 12 a^{5} b^{2} \cdot (3 b^{3} c^{2})$

Step 2

Multiply $b^{2}$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$- 12 a^{5} (b^{3} b^{2}) \cdot (3 c^{2})$

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

$- 12 a^{5} b^{3 + 2} \cdot (3 c^{2})$

Add $3$ and $2$ .

$- 12 a^{5} b^{5} \cdot (3 c^{2})$

Step 3

Multiply $3$ by $- 12$ .

$- 36 a^{5} b^{5} c^{2}$