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11:54 AM
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Q: Help me find an original for questions like "Why $(-1)^{ab} \ne [(-1)^a]^b$ when $a, b, \in \Bbb R$?"

Alex M.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...

See if these search results help: approach0.xyz/search/…Wei Zhong Nov 16 at 13:29
@WeiZhong: Whoa! Your search engine really works! It's true that the list of results is a mixed bag, but among some irrelevant ones I have also found some more relevant than the ones suggested by other users above. What I like is that even though one of the search terms is $a^{bc} = (a^b)^c$, the search engine also found a question containing $(z^a)^b \ne z^{ab}$ (notice that the relation is reversed, and that we have $\ne$ instead of $=$), another answer containing $(x^m)^n = x^{mn}$ etc.. Congratulations! This is really nice and useful! — Alex M. Nov 16 at 15:15
@AlexM. Glad to know you think it is useful. — Wei Zhong Nov 17 at 12:51
 

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