Simplify ((-5r^2s^7)/r)^3

${(\frac{- 5 r^{2} s^{7}}{r})}^{3}$

Cancel the common factor of $r^{2}$ and $r$ .

Factor $r$ out of $- 5 r^{2} s^{7}$ .

${(\frac{r (- 5 r s^{7})}{r})}^{3}$

Cancel the common factors.

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

${(\frac{r (- 5 r s^{7})}{r^{1}})}^{3}$

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

${(\frac{r (- 5 r s^{7})}{r \cdot 1})}^{3}$

Cancel the common factor.

${(\frac{r (- 5 r s^{7})}{r \cdot 1})}^{3}$

Rewrite the expression.

${(\frac{- 5 r s^{7}}{1})}^{3}$

Divide $- 5 r s^{7}$ by $1$ .

${(- 5 r s^{7})}^{3}$

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

Apply the product rule to $- 5 r s^{7}$ .

${(- 5 r)}^{3} {(s^{7})}^{3}$

Apply the product rule to $- 5 r$ .

${(- 5)}^{3} r^{3} {(s^{7})}^{3}$

Raise $- 5$ to the power of $3$ .

$- 125 r^{3} {(s^{7})}^{3}$

Multiply the exponents in ${(s^{7})}^{3}$ .

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

$- 125 r^{3} s^{7 \cdot 3}$

Multiply $7$ by $3$ .

$- 125 r^{3} s^{21}$