Why is it that everything to the ZERO power equals one?

Question

ex:

5^0= 1
234325346^0= 1

Answer 1

Each time you multiply a number by itself you increment the exponent:
A*A=A^2

Each time you divide a number by itself you decrement the exponent:
So...
(A^3)/A = A^2
(A^2)/A = A^1 = A
A/A = 1 = A^0

Hope this helps.

A

Answer 2

it's right

but in fact the best argument

if x is a number

A^x=exp(x*ln(A))
and exp(0)=1

but i don't know if you know exp and log functions lol

Answer 3

If you have a calculator try raising some number to smaller and smaller powers and see what happens.
100^.01 =1.0471
100^.001 =1.00461
100^.0000001 = 1.000000461

Answer 4

Here is another explanation

If you accept the rules of exponents then

x^a/x^a = x^(a-a) = x^0

but x^a/x^a = 1 since any number divided by itself is 1
so x^0 = 1

Answer 5

i don't know what is your level in maths..
so you can write x^a/x^a=1
but,in fact,it's wring because it's not defined for x=0
so your answer is right but in high school it's wrong...