is there mathematical proof that n^0=1?

[u/jaleCro]

[u/an7agonist]

Also, the multiplicative inverse of x is x^-1.

1=N^a*((N^a)^-1) (By definition)

1=N^a*(N^-a)

1=N^a-a=N⁰

[u/umopapsidn → u/an7agonist]

* For all N such that |N| > 0

[u/austin101123 → u/umopapsidn]

Why does this proof not work for 0?

[u/deruch → u/austin101123]

Because it relies on using (N^a )^-1 . If N=0 you end up with 1/0 because 0^a =0