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0^0

by MBA.Aspirant » Thu Jun 23, 2011 2:13 pm
0^0 = 1 or 0?

we know anything raised to the power of 0 = 1. But what of 0^0?

I'm asking cause I got a problem asking 0^x so if you plugin x=1 then 0^1 = 0. But what of x=0?
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by Ian Stewart » Thu Jun 23, 2011 2:18 pm
0^0 is not defined, for the reason you point out: for positive values of x, x^0 is always equal to 1, but 0^x is always equal to 0, so there's no way to define a value of 0^0 that will make sense. On official questions, you'll never need to consider what 0^0 is; the question will always give restrictions on the values of your unknowns so that 0^0 need not be considered.
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by MBA.Aspirant » Thu Jun 23, 2011 2:28 pm
yep its defined in the question.

x^y and |y|^x. x>1 and y<0.

but as a funny trivia try typing 0^0 in google :)

Also this article says it's = 1: https://www.facebook.com/l.php?u=http%3 ... ml&h=41c5b
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by Ian Stewart » Thu Jun 23, 2011 4:31 pm
MBA.Aspirant wrote:yep its defined in the question.

x^y and |y|^x. x>1 and y<0.

but as a funny trivia try typing 0^0 in google :)

Also this article says it's = 1: https://www.facebook.com/l.php?u=http%3 ... ml&h=41c5b
If you read that text, it makes clear there no universally agreed view on the value of 0^0. If 0^0 were defined to have a value, then the value 1 makes the most sense, but there are equally good reasons for declaring 0^0 to be an undefined quantity. Regardless, on the GMAT it doesn't matter - you'll never need to worry about it.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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