Question

HELP!
I have a question , and i need it to be where i can understand it.
why is a number, any number, is 1 when raised to the 0 power. i need it for an assessment. and i can't find a site that explains anything to me to where i can understand it enough to put it in my own words

Answer 1

Mathematics is all about patterns.
Consider the following
2^3 = 8 , no discussion there, right?
2^2 = 4
2^1 = 2
2^0 = ?? , to fit the pattern 2^0 = 1
2^-1 = 1/2
etc
I can set up the same pattern for any number.

or

(x^a)(x^0) = x^(a+0) = x^a

if (x^a)(x^0) = x^a
x^0 behaves just like the number 1

or

a^b / a^b = 1, since any number divided by itself is 1, where a^b ≠ 0

but by the rules of division of powers
a^b / a^b = a^(b-b) = a^0
so a^0 = 1

Answer 2

that helps a little, thanks. :D