I'm asking about the Zero Index which is a^0 = 1

 

can anyone explain 'mathematically' to me how this happen?

 

P.S. how does people write Superscript, Subscript and fraction number in this forum?

The Latex mode is switched with [ math] and ended with [ /math], the commands in between are Latex (there is a tutorial thread on latex somewhere in this forum). There are pocket play tricks to justify it, such as [math]a^0 = a^{1-1} = a^1 a^{-1} = a/a = 1[/math], but I'm not sure if that's what you were looking for - I certainly couldn't tell you at the moment which underlying assumptions I made for this trick to work, so it's possibly just a cyclic argument.

Edited May 17, 201114 yr by timo

nice answer, that's what i'm looking for because i made an additional math's note on power point,

 

so, needed an understanding on how those formula formed.

 

thnx.

Edited May 17, 201114 yr by Vastor

Glad it helped you. Note that the trick does not work for a=0. And indeed: If I remember correctly then [math]0^0[/math] is commonly considered as not being defined.

I'm asking about the Zero Index which is a^0 = 1

 

can anyone explain 'mathematically' to me how this happen?

 

P.S. how does people write Superscript, Subscript and fraction number in this forum?

 

It is a definition, which is consistent with exponentiation by integers and attendant relations.

[math]x^2_1[/math]