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.
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May be of interest: https://math.stackexchange.com/questions/548/explanation-of-method-for-showing-that-frac00-is-undefined – Arnaud Mortier Mar 13 '18 at 16:29
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$0^{-1}$ doesn't exist because we can't find another number $x$ such that $0x=1$.
We do have $$0=0^{1}$$

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