(-2mn^2)^(-3)/4m^(-6)n^(4)
I think you dreamed this one up!
(-2mn^2)^(-3)/4m^(-6)n^(4) = -1/(32 m^9 n^2)
\(\frac{(-2mn^2)^3}{4m^{-6}n^4}\)
\(= \frac{-8m^3n^6(m^6)}{4n^4}\)
\(= -2m^9n^2\)
