Is $0 = 0^1 = 0^2 \times 0^{-1}?$

Question

Does the above equation follow? Conversely, can you say $0^2 \times 0^{-1} = 0^1 = 0$? I apologize if this is a stupid question but it just popped in my mind.

Answer 1

$0^{-1}$ doesn't exist because we can't find another number $x$ such that $0x=1$.

We do have $$0=0^{1}$$