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There are many questions that boil down to "why is it not true that $(-1)^{ab} = [(-1)^a]^b$ (or $z^{ab} = (z^a)^b$) for $z \in \Bbb C$ and $a, b \in \Bbb R$ (or $\Bbb C$)?" and, respectively, "why is it not true that $(-1)^{a+b} = (-1)^a(-1)^b$ (or $z^{a+b} = z^a z^b$ for $z \in \Bbb C...