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

1. KingGeorge

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

2. sasogeek

make that exception, then prove for any other number

3. ParthKohli

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

4. KingGeorge

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$$

5. ParthKohli

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

6. UnkleRhaukus

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