(2b^4)^-1 = 1/(2b^4)
(x^2y^-1)^-1 = 1/(x^2y^-1) = y/x^2 <-- notice that the y had a negative exponent and so could be brought back up the numerator
x^2/(2x^3) <-- in this case, we need to subtract the exponents since the "x"s are the same base. We get
1/2*x^(2 - 3) = 1/2*x^-1 = 1/(2x)
If that's not clear, say so and I'll try to explain it better.