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

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

Step 1

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

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

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

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

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

Step 2

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

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

Step 3

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

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

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

Multiply $2$ by $5$ .

$- 32 x^{10} {(y^{3})}^{5}$

Step 4

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

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

$- 32 x^{10} y^{3 \cdot 5}$

Multiply $3$ by $5$ .

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