I just saw this equation on Apostol Calculus, Chapter 1 (the chapter about Real numbers and etc. on Theorem 1.9, right after the introduction)
If $a\neq 0$, then $\dfrac{b}{a}=ba^{-1}$
what kind of assumption do I have to make about $a^{-1}$ to prove the equation?
I'm guessing it would be $a^{-1}\times a^{+1}=a^{-1+1}=a^{0}=1$
But the book seems to tell me NOT to make any assumptions on reals (and on exponents also).
Thank you!