Simplify ab(-8a^3b^2)

$a b (- 8 a^{3} b^{2})$

Step 1

Rewrite using the commutative property of multiplication.

$- 8 a b (a^{3} b^{2})$

Step 2

Multiply $a$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

$- 8 (a^{3} a) b \cdot b^{2}$

Multiply $a^{3}$ by $a$ .

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

$- 8 (a^{3} a^{1}) b \cdot b^{2}$

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

$- 8 a^{3 + 1} b \cdot b^{2}$

Add $3$ and $1$ .

$- 8 a^{4} b \cdot b^{2}$

Step 3

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

Move $b^{2}$ .

$- 8 a^{4} (b^{2} b)$

Multiply $b^{2}$ by $b$ .

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

$- 8 a^{4} (b^{2} b^{1})$

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

$- 8 a^{4} b^{2 + 1}$

Add $2$ and $1$ .

$- 8 a^{4} b^{3}$