# 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 highschool, and now in cegep.

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

Homework Helper
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 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.

#### matt grime

Homework Helper
gnomedt said:
Alternatively, since na+b=nanb, then it must be that

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

na=na+0=nan0, 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!!

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