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

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

Step 1

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

Apply the product rule to $- 3 a^{2} b^{3}$ .

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

Apply the product rule to $- 3 a^{2}$ .

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

Step 2

Raise $- 3$ to the power of $2$ .

$9 {(a^{2})}^{2} {(b^{3})}^{2}$

Step 3

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

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

$9 a^{2 \cdot 2} {(b^{3})}^{2}$

Multiply $2$ by $2$ .

$9 a^{4} {(b^{3})}^{2}$

Step 4

Multiply the exponents in ${(b^{3})}^{2}$ .

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

$9 a^{4} b^{3 \cdot 2}$

Multiply $3$ by $2$ .

$9 a^{4} b^{6}$