law of indices

[Vastor]

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?

[timo]

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, 2011 by timo

[Vastor]

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, 2011 by Vastor

[timo]

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.

[DrRocket]

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.

[Vastor]

[math]x^2_1[/math]