∀ {E : Type} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f g : E → ℂ} {s : Set E},
  AnalyticOn ℂ f s → AnalyticOn ℂ g s → (∀ z ∈ s, f z ∈ Complex.slitPlane) → AnalyticOn ℂ (fun z => f z ^ g z) s