Simplify ((-3r^6s^3)/r)^2

${(\frac{- 3 r^{6} s^{3}}{r})}^{2}$

Step 1

Cancel the common factor of $r^{6}$ and $r$ .

Factor $r$ out of $- 3 r^{6} s^{3}$ .

${(\frac{r (- 3 r^{5} s^{3})}{r})}^{2}$

Cancel the common factors.

Raise $r$ to the power of $1$ .

${(\frac{r (- 3 r^{5} s^{3})}{r^{1}})}^{2}$

Factor $r$ out of $r^{1}$ .

${(\frac{r (- 3 r^{5} s^{3})}{r \cdot 1})}^{2}$

Cancel the common factor.

${(\frac{r (- 3 r^{5} s^{3})}{r \cdot 1})}^{2}$

Rewrite the expression.

${(\frac{- 3 r^{5} s^{3}}{1})}^{2}$

Divide $- 3 r^{5} s^{3}$ by $1$ .

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

Step 2

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

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

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

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

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

Step 3

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

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

Step 4

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

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

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

Multiply $5$ by $2$ .

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

Step 5

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

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

$9 r^{10} s^{3 \cdot 2}$

Multiply $3$ by $2$ .

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