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

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

Step 1

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

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

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

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

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

Step 2

Raise $- 2$ to the power of $5$ .

$- 32 {(x^{3})}^{5} {(y^{2})}^{5}$

Step 3

Multiply the exponents in ${(x^{3})}^{5}$ .

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

$- 32 x^{3 \cdot 5} {(y^{2})}^{5}$

Multiply $3$ by $5$ .

$- 32 x^{15} {(y^{2})}^{5}$

Step 4

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

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

$- 32 x^{15} y^{2 \cdot 5}$

Multiply $2$ by $5$ .

$- 32 x^{15} y^{10}$