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

1. Jun 16, 2006

### 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 highschool, and now in cegep.

2. Jun 16, 2006

### DeadWolfe

For an integer a:

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

3. Jun 16, 2006

### Mozart

Hehe math is so cool. Thanks.

4. Jun 16, 2006

### 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.

5. Jun 17, 2006

### gnomedt

Alternatively, since na+b=nanb, then it must be that na=na+0=nan0, so n0 = 1.

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

6. Jun 17, 2006

### matt grime

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

7. May 1, 2011

### joaquince

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

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook