Find the Product (3a^2b^4)(-8ab^3)

$(3 a^{2} b^{4}) (- 8 a b^{3})$

Step 1

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

Move $a$ .

$3 (a \cdot a^{2}) b^{4} (- 8 b^{3})$

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

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

$3 (a^{1} a^{2}) b^{4} (- 8 b^{3})$

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

$3 a^{1 + 2} b^{4} (- 8 b^{3})$

Add $1$ and $2$ .

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

Step 2

Multiply $b^{4}$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$3 a^{3} (b^{3} b^{4}) \cdot - 8$

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

$3 a^{3} b^{3 + 4} \cdot - 8$

Add $3$ and $4$ .

$3 a^{3} b^{7} \cdot - 8$

Step 3

Multiply $- 8$ by $3$ .

$- 24 a^{3} b^{7}$