Why is 3 to the zero power equal to one?
2007-04-11 04:29:19 · 6 answers · asked by egg_sammash 5 in Education & Reference ➔ Homework Help
1 is the neutral element of multiplication as 0 is the neutral element of addition.
Neutral element means that this number doing the defined operation with any other number will result in the original other number.
If you raise any number x to a power n - with n>0 - you multiply this number x n times with itself.
If you raise any number x to a power 1/q - with q>0 - you extract the q root of x.
Extracting the root is the inverse operation of raising to the power.
Now if n=0 you multiply x 0 times with itself => there is no x you can multiply at all and this does not help you at all.
So the best way to figure out what happens for n=0 is by looking what happens if q approaches infinity. This one is possible to solve through examining the limit and the solution is 1.
2007-04-11 11:04:26 · answer #1 · answered by ab1609 5 · 2⤊ 0⤋
Its a rule. Any number to the zero power is equal to one.
2007-04-11 11:34:11 · answer #2 · answered by rass 1 · 0⤊ 0⤋
Anytime you have any number to the power of zero it will always be 1. I don't know why, I have just always known that that was a rule.
2007-04-11 11:47:43 · answer #3 · answered by debbie_75052 4 · 0⤊ 0⤋
Because anything to the zero power is 1. It's a rule. ^^ Don't you love mathematical rules?
2007-04-11 11:33:34 · answer #4 · answered by Heidi L 2 · 1⤊ 0⤋
I don't know why. I just know Mr.K says its a rule and to live with it.
Dont over-analyze things^^
2007-04-11 16:29:31 · answer #5 · answered by Elley 3 · 0⤊ 1⤋
I don't know, it's one of life's mysteries.
2007-04-11 12:01:07 · answer #6 · answered by Anonymous · 1⤊ 0⤋