why is a zero exponent equal to 1?

Answer 1

Hope you have your thinking cap on:

n^x
--- = n^(x-y)
n^y

for all n, x, and y. So for example,
3^4
--- = 3^(4-2) = 3^2
3^2


3^4
--- = 3^(4-3) = 3^1
3^3


Now suppose we have the fraction:
3^4
---
3^4

This fraction equals 1, because the numerator and the denominator are the same. If we apply the law of exponents, we get:
3^4
1 = --- = 3^(4-4) = 3^0
3^4

So 3^0 = 1.
We can plug in any in number in the place of three, and that number raised to the zero power will still be 1. In fact, the whole proof works if we just plug in x for 3:

x^4
x^0 = x^(4-4) = --- = 1
x^4

Yeah, that's just horrible!
It's easier to just picutre a sequence of numbers like
5^3 = 125
5^2 = 25
5^1 = 5
5^0 = 1
5^-1 = 1/5
5^-2 = 1/25

Notice that with each incrment of the exponent, the number is multiplied by 5. As the exponent decrements, the number is divided by 5. And this number, at it's base, is 1! So x^0 has to be 1, becuase that's just what that particular notation means.

Answer 2

^----man that's hardcore explaning

i had a simple:

because you are going into fractions at 0

3^2 = 3 x 3 = 9
3^1 = 3
3^0 = 3 / 3 = 1
3^ -1 = 3 x 1/3 = .33

Answer 3

Coz both zero exponent and one is equal to some Crack-head, who simply created this unrealistic s.h.i.t formulas when Doped with weeds.

Answer 4

it doesnt know if it is a posivite or a negative....