Find the Product -7(-a^2)^2(-b^3)

$- 7 {(- a^{2})}^{2} (- b^{3})$

Rewrite using the commutative property of multiplication.

$- 7 \cdot - 1 {(- a^{2})}^{2} b^{3}$

Multiply $- 7$ by $- 1$ .

$7 {(- a^{2})}^{2} b^{3}$

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

$7 ({(- 1)}^{2} {(a^{2})}^{2}) b^{3}$

Raise $- 1$ to the power of $2$ .

$7 (1 {(a^{2})}^{2}) b^{3}$

Multiply ${(a^{2})}^{2}$ by $1$ .

$7 {(a^{2})}^{2} b^{3}$

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

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

$7 a^{2 \cdot 2} b^{3}$

Multiply $2$ by $2$ .

$7 a^{4} b^{3}$