@JyrkiLahtonen @RRL @rschwieb @XanderHenderson @Did: I request to close
this bad question, because it is ridiculously misleading in claiming that the poofs given in the question are actually meaningful, when they are just nonsensical. Specifically, it makes zero mathematical sense to prove a^0 = 1 by appealing to a^m/a^m = a^(m−m), nor by appealing to a^(m+0) = a^m·a^0.
This 'answer' is no better.