Simplify ((-4r^5s^3)/r)^3

${(\frac{- 4 r^{5} s^{3}}{r})}^{3}$

Step 1

Cancel the common factor of $r^{5}$ and $r$ .

Factor $r$ out of $- 4 r^{5} s^{3}$ .

${(\frac{r (- 4 r^{4} s^{3})}{r})}^{3}$

Cancel the common factors.

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

${(\frac{r (- 4 r^{4} s^{3})}{r^{1}})}^{3}$

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

${(\frac{r (- 4 r^{4} s^{3})}{r \cdot 1})}^{3}$

Cancel the common factor.

${(\frac{r (- 4 r^{4} s^{3})}{r \cdot 1})}^{3}$

Rewrite the expression.

${(\frac{- 4 r^{4} s^{3}}{1})}^{3}$

Divide $- 4 r^{4} s^{3}$ by $1$ .

${(- 4 r^{4} s^{3})}^{3}$

Step 2

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

Apply the product rule to $- 4 r^{4} s^{3}$ .

${(- 4 r^{4})}^{3} {(s^{3})}^{3}$

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

${(- 4)}^{3} {(r^{4})}^{3} {(s^{3})}^{3}$

Step 3

Raise $- 4$ to the power of $3$ .

$- 64 {(r^{4})}^{3} {(s^{3})}^{3}$

Step 4

Multiply the exponents in ${(r^{4})}^{3}$ .

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

$- 64 r^{4 \cdot 3} {(s^{3})}^{3}$

Multiply $4$ by $3$ .

$- 64 r^{12} {(s^{3})}^{3}$

Step 5

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

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

$- 64 r^{12} s^{3 \cdot 3}$

Multiply $3$ by $3$ .

$- 64 r^{12} s^{9}$