Evaluate (2a^2b)(4ab^2)

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

Step 1

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

Move $a$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Step 2

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

Move $b^{2}$ .

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

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

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

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

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

$2 a^{3} b^{2 + 1} \cdot 4$

Add $2$ and $1$ .

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

Step 3

Multiply $4$ by $2$ .

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