[tex](\frac{8s^{-3}t^{-2}}{4st^{-1}})^{-1}=[/tex]
divide numbers 8/4=2
[tex](\frac{2s^{-3}t^{-2}}{st^{-1}})^{-1}=[/tex]
apply rule [tex]a^{-n}=\frac{1}{a^n}[/tex]
[tex](\frac{2}{st^{-1}*s^{3}t^{2}})^{-1}=[/tex]
sum up the exponents
[tex](\frac{2}{s^4t})^{-1}=[/tex]
one more negative exponent flip
[tex]\frac{1}{\frac{2}{s^4t}}=[/tex]
simplify double fraction
[tex]\frac{s^4t}{2}[/tex]
