Simplify (-3x^2y^5)^2

${(- 3 x^{2} y^{5})}^{2}$

Step 1

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

Apply the product rule to $- 3 x^{2} y^{5}$ .

${(- 3 x^{2})}^{2} {(y^{5})}^{2}$

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

${(- 3)}^{2} {(x^{2})}^{2} {(y^{5})}^{2}$

Step 2

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

$9 {(x^{2})}^{2} {(y^{5})}^{2}$

Step 3

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

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

$9 x^{2 \cdot 2} {(y^{5})}^{2}$

Multiply $2$ by $2$ .

$9 x^{4} {(y^{5})}^{2}$

Step 4

Multiply the exponents in ${(y^{5})}^{2}$ .

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

$9 x^{4} y^{5 \cdot 2}$

Multiply $5$ by $2$ .

$9 x^{4} y^{10}$