rw [← Real.rpow_mul (by positivity)]
A C₁ C₂ : ℝ
Apos : 0 < A
C₁pos : 0 < C₁
C₂pos : 0 < C₂
hA : A ≤ 1 / 2 * (C₁ / (C₂ * 2)) ^ 4
⊢ (A ^ (1 / 4)) ^ 4 < (C₁ / (C₂ * 2)) ^ 4
A C₁ C₂ : ℝ
Apos : 0 < A
C₁pos : 0 < C₁
C₂pos : 0 < C₂
hA : A ≤ 1 / 2 * (C₁ / (C₂ * 2)) ^ 4
⊢ A ^ (1 / 4 * 4) < (C₁ / (C₂ * 2)) ^ 4