Simplify (-2r^2s^0)(rs^4)^2

$(- 2 r^{2} s^{0}) {(r s^{4})}^{2}$

Step 1

Anything raised to $0$ is $1$ .

$- 2 r^{2} \cdot 1 {(r s^{4})}^{2}$

Step 2

Multiply $- 2$ by $1$ .

$- 2 r^{2} {(r s^{4})}^{2}$

Step 3

Apply the product rule to $r s^{4}$ .

$- 2 r^{2} (r^{2} {(s^{4})}^{2})$

Step 4

Multiply $r^{2}$ by $r^{2}$ by adding the exponents.

Move $r^{2}$ .

$- 2 (r^{2} r^{2}) {(s^{4})}^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 r^{2 + 2} {(s^{4})}^{2}$

Add $2$ and $2$ .

$- 2 r^{4} {(s^{4})}^{2}$

Step 5

Multiply the exponents in ${(s^{4})}^{2}$ .

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

$- 2 r^{4} s^{4 \cdot 2}$

Multiply $4$ by $2$ .

$- 2 r^{4} s^{8}$