Maxima always simplifies
exp(z)^a --> exp(a*z)
In general this is only correct for -%pi < imagpart(z) <= %pi or a an integer.
This is an example with z = 3/2*%i*%pi and a = 1/2. First we calculate exp(z)^a:
The result for exp(a*z) differs by the sign:
In the first example Maxima immediately simplifies exp(3/2*%i*%pi) --> -%i. Therefore, the simplification exp(z)^a is not applied.
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