Porównaj liczby. a) 22³³ i 33²² b)333⁴⁴⁴ i 444³³³ Proszę o dokładne rozwiązanie bez użycia kalkulatora :P Będę usuwał takie odpowiedzi :D

a) 22³³ i 33²² * - mnożenie 22³³ = (2 * 11)³³ = 2³³ * 11³³ = (2³)¹¹ * (11³)¹¹ = 8¹¹ * (11³)¹¹ = (8 * 11³)¹¹ 33²² = (3 * 11)²² = 3²² * 11²² = (3²)¹¹ * (11²)¹¹ = 9¹¹ * (11²)¹¹ = (9 * 11²)¹¹ (8 * 11³)¹¹ > (9 * 11²)¹¹ b) 333⁴⁴⁴ i 444³³³ 333⁴⁴⁴ = (3 * 111)⁴⁴⁴ = 3⁴⁴⁴ * 111⁴⁴⁴ = (3⁴)¹¹¹ * (111⁴)¹¹¹ = (3⁴ * 111⁴)¹¹¹ = (81 * 111⁴)¹¹¹ 444³³³ = (4 * 111)³³³ = 4³³³ * 111³³³ = (4³)¹¹¹ * (111³)¹¹¹= (4³ * 111³)¹¹¹ = (64 * 111³)¹¹¹ (81 * 111⁴)¹¹¹ > (64 * 111³)¹¹¹