If x^a*x^b = 1 and x ≠ -1, 1, then a + b = ?

And I'd add that I find some prep books make far too big a deal about technicalities about the number zero, technicalities the GMAT never actually tests. If you go through, for example, every DS question in OG12 and the green Quant Review book, there isn't a single question where you'd get a different answer if you forgot to consider zero.

Of course the number 0 can show up in questions, just as any other number can, but you won't ever need to concern yourself with what 0^0 might mean, or what 0! (zero factorial) is equal to. The GMAT isn't interested in obscure technicalities like those. So if you see x^0 on the GMAT, you can safely assume that it is equal to 1. If you see n! on the GMAT, you can assume n is positive. If you see the phrase "x is an even integer", it will never matter if x might be 0 (zero is just like any other even integer where addition, subtraction or multiplication are concerned). And if you see the phrase "the integer x is divisible by 7", it will never matter if x might be 0 (zero is just like any other multiple of 7 as far as divisibility properties go).

The only property of zero I see tested frequently is the following: if you multiply numbers together, and the result is zero, you must have multiplied by zero. So if abc = 0, at least one of a, b or c must be zero. Or if (x-1)(x-2) = 0, then either x - 1 = 0 or x - 2 = 0, so x is either 1 or 2. Beyond that one (very important) property, I can't think of any situations on the GMAT where you'd need to consider zero in any special way. I have seen quite a few prep company questions where zero is used as a 'trap', but I find those questions very unrealistic for the most part.

@IanStewart - You are absolutely right about my typo. I fixed it in the original post. Thanks for pointing it out!

@bhavinp: I believe that 0^0 is undefined. Therefore, I am not sure whether we should assume that it equals to 0 or 1 or any other number.

@Ian: If we assume that the correct answer is indeed the official answer, C, then I still can't understand how can we ensure that x isn't 0. I understand that probably this won't be a GMAT question that someone would possibly face, but as far as mathematics is concerned, should't the answer be E?

First, you definitely will never need to worry about this issue on the GMAT, so it isn't really worth spending much time on, but in any case, logically it doesn't change the answer if you consider the possibility that x=0 here. We know that

x^(a + b) = 1

Can x be equal to 0? Certainly not. 0^(a+b) is always either equal to 0 (when a+b is positive), or is undefined (when a+b is 0 or less). So 0^(a+b) is never equal to 1, and the equation above just won't ever be true if x=0.

@sonygmat, x cannot be 0, because if x were 0 then x^(a+b) could not equal 1. The only way the answer could be E is if there were some value other than 0 for (a+b) such that x^(a+b) equals 1.

The more important point as Ian mentioned is that the GMAT does not test this concept.

(x^a)(x^b)=1
x^(a+b)=1
which is possible only when a+b=0

in case x=0 then it will be non determinate form while we have expression equals to 1/
ans is C

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.