(a) For ring (R, +, •) and each d e R, we define al = a, and dn+l = and, for all n ∈ Z+. Prove that for all m, n ∈ Z+, (am)(an) = am+n and (am)n = amn.
(b) Can you suggest how we might define a° or a-n, n ∈ Z+, including any necessary conditions that R must satisfy for these definitions to make sense?