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It doesn'tFive to "no power" is, by convention, the same as five raised to the power of one (51), which equals five.

Five to the power of zero (50), on the other hand, is, by convention, equal to one, because any number raised to the power of zero is one. Don't try too hard to conceptualize a number raised to the power of zero. It evaluates to one merely because that is the convention.

I'm sure that's what you meant when you said "no power."

Just a convention?I would disagree with the above answer and say that it's more than a convention. Some of the rules for exponentiation may seem strange at first (eg 5-1, 51/2). But if you change the rules, then axioms such as xa+b = xa * xb no longer hold. That means that if you ever do a proof involving these axioms, you get bogged down in a case analysis, i.e. different proofs for different values of x. So, while you are of course welcome to invent your own functions, they won't be as useful as the versions that are already defined.
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Q: Why does 5 to no power equal 1?
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Related questions

What is 5 to the power of 1 equal?

51 = 5


What does 1 to the power of 5 equal?

One.


What does 5 to the negative one power equal?

5-1 = 1/5 or 0.2


What does 1 squared by 5 equal?

There is no such thing as 1 SQUARED by 5. It is actually 1 to the 5th power, which is 1.


What is 10 to the power of negative 5?

0.00001 or 1 over 100,000


What does 5 to the power -2 equal?

7


What is 5 to the power of negative six?

it is equal to 1/5^6 which equals 0.000064


What is 5 to the power of 3 times 5 to the power of 2 but written as a power of 5?

5 to the power of three times 5 to the power of 2 is equal to 5 to the power of 5. We know this because A^a times A^b equals A^(a+b). We know this by solving the problem manually. 5 to the power of 3 is equal to 5*5*5 and 5 to the power of 2 is equal to 5*5. when you multiply them, it becomes 5*5*5*5*5 which is equal to 5 to the power of 5.


What does 10 to the negative 1 equal?

10-1 = 1/10 A number raised to a negative power is equal to the reciprocal of the number raised to the power. So a-b = (1/a)b = 1/ab


Does 8 to the power of 8 equal 1?

8 to the power of 8 = 8x8x8x8x8x8x8x8 and does not equal 1 but 1 to the power of 8 does equal 1


What does -5 to the -3 power equal?

-2


What quotients are equal to 4 to the negative fifth power?

Well, honey, any quotient equal to 4 to the negative fifth power is just 1 over 4 to the fifth power, which simplifies to 1 over 1024. So, grab your calculator and divide 1 by 1024, and you'll have your answer faster than you can say "Golden Girls marathon."