How do you prove that a^0 = 1 for non-zero a?

[thinkies]

Homework Statement

Prove that a^0 = 1 if a is not equal to 0.

Homework Equations

The Attempt at a Solution

Well,since a is not equal to 0, I replace it with another number.

(1^0)^0 = 1

(6^0)^0 = 1

ETC

Is this enough to prove that a^0 = 1 if a is not equal to 0.Even thought its a basic and easy question...im doubting.

Thx

 

[thinkies]

hhmmm any1?...

 

[Dick]

You haven't 'proved' anything. You just wrote down some numbers. What's your definition of a^x? If it's e^(log(a)*x) the answer is pretty easy, just take the log of both sides. To prove something you need a precise definition of the thing you are trying to prove. What does a^x mean?

 

[Dick]

Are you just assuming the laws of exponents? Like (a^n)*(a^m)=a^(n+m)? If so, then set m=0 and solve for a^m.

 

[thinkies]

Are you just assuming the laws of exponents? Like (a^n)*(a^m)=a^(n+m)? If so, then set m=0 and solve for a^m.

Thanks, i though about doing that before, don't know what came up in mind.