There are many questions that boil down to "why is it not true that $(-1)^{ab} = (-1)^a (-1)^b$ (or $z^{ab} = z^a z^b$) for $z \in \Bbb C$ and $a, b \in \Bbb R$ (or $\Bbb C$)?". Can you please help me to find one such archetypical example that I should use as "original" when closing this ty...