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.

  • 14
    $\begingroup$ I see that some people have already jumped to close my question as off-topic: hold your horses, please! This is the only place on the internet where such a question makes sense to be asked (where else would you want me to ask it: on Facebook, on Reddit, on Slashdot?), and it concerns the good management of question closing on MSE, which makes it perfectly on-topic - provided the reader be willing to reason a bit. $\endgroup$
    – Alex M.
    Commented Nov 15, 2016 at 15:21
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    $\begingroup$ It's not clear to me why somebody would vote to close this question as "off-topic." It may be a bit localized, but really the traffic on meta is not that high that we need to be super-strict. $\endgroup$
    – quid Mod
    Commented Nov 15, 2016 at 15:23
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    $\begingroup$ Um, $z^az^b=z^{a+b}$, not $z^{ab}$. $\endgroup$ Commented Nov 15, 2016 at 15:38
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    $\begingroup$ @BarryCipra: I can't understand why that happened... $\endgroup$
    – Alex M.
    Commented Nov 15, 2016 at 15:44
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    $\begingroup$ Maybe one of these: math.stackexchange.com/questions/linked/438?lq=1 which are all linked to this one (which is probably the best target for questions of the second type): math.stackexchange.com/questions/438/… $\endgroup$ Commented Nov 15, 2016 at 16:30
  • $\begingroup$ @NajibIdrissi: The post that you link to seems to be the closest match so far, even though not exactly what I was looking for. How did you know about coming up with the other link, the one with the word "linked" in it? What's its general syntax? Where do "438" and "lq=1" come from? $\endgroup$
    – Alex M.
    Commented Nov 15, 2016 at 16:58
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    $\begingroup$ You can try to search on approach0.xyz/search $\endgroup$
    – Watson
    Commented Nov 15, 2016 at 17:00
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    $\begingroup$ When you're on a question that has other questions linked to it, on the sidebar (on a desktop browser) there is a list of linked questions, and a link saying "see more linked questions…". $\endgroup$ Commented Nov 15, 2016 at 17:30
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    $\begingroup$ Not exactly the same issue, but implicitly addressed in For which complex $a$, $b$, $c$ does $(a^b)^c = a^{bc}$ hold? (If there's an older/more famous question covering this rule of exponents, I'd be interested to know.) $\endgroup$ Commented Nov 15, 2016 at 18:12
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    $\begingroup$ See if these search results help: approach0.xyz/search/… $\endgroup$
    – Wei Zhong
    Commented Nov 16, 2016 at 13:29
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    $\begingroup$ @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! $\endgroup$
    – Alex M.
    Commented Nov 16, 2016 at 15:15
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    $\begingroup$ @AlexM. Glad to know you think it is useful. $\endgroup$
    – Wei Zhong
    Commented Nov 17, 2016 at 12:51
  • $\begingroup$ Consider using the tag faq for the target question. $\endgroup$ Commented Nov 27, 2016 at 19:05
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    $\begingroup$ @WeiZhong: Maybe you could make an ad for your search engine for community promotion ads (see meta.math.stackexchange.com/q/22419 for the rough guidelines for this year's) so that more people would be aware of it even without reading Meta. =) $\endgroup$
    – user21820
    Commented Nov 28, 2016 at 11:39
  • $\begingroup$ @user21820 Hi, thank you so much for this suggestion. I have posted an answer there: meta.math.stackexchange.com/questions/22419/… . I love the feeling of creating a useful tool. $\endgroup$
    – Wei Zhong
    Commented Nov 28, 2016 at 16:35


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