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!
Exponents theory
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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
(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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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.
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.