Prove that any number $\huge n $ to the power 0 is equal to one.

$\huge : n^0=1 $

Question

Prove that any number $\huge n $ to the power 0 is equal to one.

$\huge : n^0=1 $

kinggeorge · Answer

What about $n=0$? That's undefined.

sasogeek · Answer

make that exception, then prove for any other number

parthkohli · Answer

Do you know that $\Large \color{purple}{\rightarrow x^n \div x^1 = x^{n - 1} }$

kinggeorge · Answer

We know that $n^1=n$ and $n^{-1}={1 \over n}$ for all $n$. If we multiply together,$$n^1 \cdot n^{-1}=n^{1-1}=n^0$$$$n\cdot{1 \over n}={n \over n}=1$$So $n^0=1$

parthkohli · Answer

$\Large \color{purple}{\rightarrow x^1 = x }$

$\Large \color{purple}{\rightarrow x^1 \div x^1 = 1 }$ as they cancel out.
Also, x^1 over x^1 = x^0


$\Large \color{purple}{\rightarrow x^0 = 1 = x^1 \div x^1 }$

unklerhaukus · Answer

nice answers

across · Answer

@KingGeorge, I would say that for the case where $n=0$ is more subjective than it is undefined nowadays. ;)