Why ##a^0=1##?

[Mike_bb]

Hello!

I have problem in understanding why $a^0=1$.

I represent $a^x$ as $1*a*a*a*a*...*a$ (x times)

Why $a^0=1$? Why is $a^0$ not equal to $0$?

Thanks.

 

[Ibix]

It's consistent with $a^{n+1}=a\cdot a^n$

 

[Ibix]

Or, more generally, $a^{n+m}=a^na^m$ implies $a^0=1$, because otherwise $a^{n+0}\neq a^n$.

 

[martinbn]

Hello!

I have problem in understanding why $a^0=1$.

I represent $a^x$ as $1*a*a*a*a*...*a$ (x times)

Why $a^0=1$? Why is $a^0$ not equal to $0$?

Thanks.

Well if your $x$ is zero, then you will have no $a$'s, so just the $1$ in the begining.