Q:

Why is it that $2\times 0 = 0$, but $2^0= 1$?

Why is it that $2\times 0 = 0$, but $2^0= 1$?

I don't understand the reason behind it. If anyone explain it then it will be very appreciated. I know how multiplication, addition, and division work, but this one always puts my mind back to null.

A:

Because $\;2 \cdot 3 = \color{red}{0} + \underbrace{2 + 2 + 2}_{3\;\text{times}}\;$, while $\;2^3 = \color{red}{1} \cdot \underbrace{2 \cdot 2 \cdot 2}_{3\;\text{times}}\;$.

A:

Alternatively: $2\cdot0=2\cdot(1-1)=2-2=0$; $2^0=2^{1-1}=\frac22=1$.

