simp only [hasTemperateGrowth_smul_apply, norm_smul]
F : Type u_1
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedSpace ℂ F
inst✝ : CompleteSpace F
k n : ℕ
f : 𝓢(ℝ, F)
ξ : ℝ
⊢ ‖𝓕 (fun x => ((hasTemperateGrowth_smul (_ : Function.HasTemperateGrowth fun x => x ^ n)) f) x) ξ‖ * |ξ| ^ k *
      (2 * π) ^ k =
    ‖(2 * ↑π * I * ↑ξ) ^ k •
        𝓕 (fun x => ((hasTemperateGrowth_smul (_ : Function.HasTemperateGrowth fun x => x ^ n)) f) x) ξ‖
F : Type u_1
inst✝² : NormedAddCommGroup F
inst✝¹ : NormedSpace ℂ F
inst✝ : CompleteSpace F
k n : ℕ
f : 𝓢(ℝ, F)
ξ : ℝ
⊢ ‖𝓕 (fun x => x ^ n • f x) ξ‖ * |ξ| ^ k * (2 * π) ^ k = ‖(2 * ↑π * I * ↑ξ) ^ k‖ * ‖𝓕 (fun x => x ^ n • f x) ξ‖