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

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

Apply the product rule to $a^{2} b$ .

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

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

Move $b^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply the exponents in ${(a^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $2$ by $2$ .

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

Multiply $a$ by $a^{4}$ by adding the exponents.

Move $a^{4}$ .

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

Multiply $a^{4}$ by $a$ .

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

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

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

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

Add $4$ and $1$ .

$- a^{5} b^{3}$