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Exponents theory

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by metallicafan » Thu Jun 28, 2012 9:09 am
I have a question about exponents?

Is zero the only exponent in which two distintc bases produce the same result = 1?

For example: 3^0 = 1 ; 5^0= 1, etc.

Is the only exponent with that property?

Thanks!
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by Anurag@Gurome » Thu Jun 28, 2012 9:25 am
Yes.
(Any number)^0 = 1
However 0^0 is an exceptional case, which is equal to either 0 or 1 depending upon the context.

Also (1)^(Any number) = 1
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by KapTeacherEli » Thu Jun 28, 2012 11:11 am
Good question!

As Anurag said, ^0 is the only way to get "1" as the result of raising a number other than 1 to a power. However, It is NOT the only way to equate two exponents with the same power but different bases. Remember, even powers on exponents remove the negative sign on the base. So, 2^2 = (-2)^2 = 4, and 3^4 = (-3)^4 = 81.
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