EDB — 202

[202] Let \(F\) be a field; given \(𝛼≠ 0\) and \(h∈ℕ\) consider the recursive definition of exponentiation \(𝛼^ h\) defined from \(𝛼^ 0=1\) and \(𝛼^{(n+1)}= 𝛼^ n ⋅ 𝛼\); then prove that \(𝛼^{h+k}=𝛼^ h𝛼^ k\) and \((𝛼^ h)^ k=𝛼^{(hk)}\) for every \(k,h∈ℕ\).