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

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

Rewrite using the commutative property of multiplication.

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 a b$ .

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

Apply the product rule to $2 a$ .

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

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

Move $a^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

Move $b^{3}$ .

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

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

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

Add $3$ and $2$ .

$3 (2^{2} a^{4} b^{5})$

Raise $2$ to the power of $2$ .

$3 (4 a^{4} b^{5})$

Multiply $4$ by $3$ .

$12 a^{4} b^{5}$