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 $z \in \Bbb C$ and $a, b \in \Bbb R$ (or $\Bbb C$)?".
Can you please help me to find one instance of each such archetypical example that I should use as "original" when closing this type of questions as duplicates? I've tried my best with Google, but it seems that I haven't chosen the good search terms, despite having seen this kind of questions popping up several times already.