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

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Combine $\frac{1}{r^{3}}$ and $s^{4}$ .

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

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 4

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

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

Step 5

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

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

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

Multiply $3$ by $4$ .

$\frac{r^{12}}{{(s^{4})}^{4}}$

Step 6

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

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

$\frac{r^{12}}{s^{4 \cdot 4}}$

Multiply $4$ by $4$ .

$\frac{r^{12}}{s^{16}}$