Simplify ((3r^-2s)/(t^-1))^-1

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

Step 1

Move $r^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Move $t^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

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

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