In MATLAB, a^b is defined to be equivalent to exp(log(a)*b). When a is negative the log is complex with a πι component and if b is not an integer then the exp() of the πι*b is going to be complex.
In practice you can tell from timings that for at least some integer values a^b is not implemented through logs: for example a^2 has timing the same as a*a, but the principle is the same.
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