Simplify ab(-4ab^3)

$a b (- 4 a b^{3})$

Step 1

Rewrite using the commutative property of multiplication.

$- 4 a b (a b^{3})$

Step 2

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a$ .

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

Step 3

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

Move $b^{3}$ .

$- 4 a^{2} (b^{3} b)$

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

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

$- 4 a^{2} (b^{3} b^{1})$

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

$- 4 a^{2} b^{3 + 1}$

Add $3$ and $1$ .

$- 4 a^{2} b^{4}$