Simplify (s/(r^2))^(-3/4)

${(\frac{s}{r^{2}})}^{- \frac{3}{4}}$

Step 1

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

${(\frac{r^{2}}{s})}^{\frac{3}{4}}$

Step 2

Apply the product rule to $\frac{r^{2}}{s}$ .

$\frac{{(r^{2})}^{\frac{3}{4}}}{s^{\frac{3}{4}}}$

Step 3

Multiply the exponents in ${(r^{2})}^{\frac{3}{4}}$ .

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

$\frac{r^{2 (\frac{3}{4})}}{s^{\frac{3}{4}}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{r^{2 \frac{3}{2 (2)}}}{s^{\frac{3}{4}}}$

Cancel the common factor.

$\frac{r^{2 \frac{3}{2 \cdot 2}}}{s^{\frac{3}{4}}}$

Rewrite the expression.

$\frac{r^{\frac{3}{2}}}{s^{\frac{3}{4}}}$