Simplify a^3b^2*(4ab^3)

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

Move $a$ .

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

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

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

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

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

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

Add $1$ and $3$ .

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

Step 3

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

Move $b^{3}$ .

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

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

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

Add $3$ and $2$ .

$4 a^{4} b^{5}$