Why is (n^0=1)? where n is any positive number

[Mozart]

I just can't justify this in my simple mind. I just always accepted it because I was told that it is equal to 1 throughout high school, and now in cegep.

 

[DeadWolfe]

For an integer a:

n^0 = n^(a-a) = n^a(n^-a) = (n^a)/(n^a) = 1

 

[Mozart]

Hehe math is so cool. Thanks.

 

[matt grime]

Have a search for lots of posts on this topic on these forums; it is essentially a convention that allows us to coherently extend a definitions of powers.

 

[gnomedt]

Alternatively, since n^a+b=n^an^b, then it must be that n^a=n^a+0=n^an⁰, so n⁰ = 1.

Except for n = 0, of course. There's a whole thread on that.

 

[matt grime]

Alternatively, since n^a+b=n^an^b, then it must be that

If we want to extend the definition from its natural domain consistently

n^a=n^a+0=n^an⁰, so n⁰ = 1.

Except for n = 0, of course. There's a whole thread on that.

 

[joaquince]

1 = (5^7)/(5^7)= 5^(7-7) = 1 Easy!