Find the Product (-3r^3s^5)^2-r^6s^10

${(- 3 r^{3} s^{5})}^{2} - r^{6} s^{10}$

Step 1

Simplify each term.

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

Apply the product rule to $- 3 r^{3} s^{5}$ .

${(- 3 r^{3})}^{2} {(s^{5})}^{2} - r^{6} s^{10}$

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

${(- 3)}^{2} {(r^{3})}^{2} {(s^{5})}^{2} - r^{6} s^{10}$

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

$9 {(r^{3})}^{2} {(s^{5})}^{2} - r^{6} s^{10}$

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

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

$9 r^{3 \cdot 2} {(s^{5})}^{2} - r^{6} s^{10}$

Multiply $3$ by $2$ .

$9 r^{6} {(s^{5})}^{2} - r^{6} s^{10}$

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

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

$9 r^{6} s^{5 \cdot 2} - r^{6} s^{10}$

Multiply $5$ by $2$ .

$9 r^{6} s^{10} - r^{6} s^{10}$

Step 2

Subtract $r^{6} s^{10}$ from $9 r^{6} s^{10}$ .

$8 r^{6} s^{10}$