Question

comparare 55 la puterea 33 si 9 la putera 123

Answer 1

55^33=(5×11)^33=5^33×11^33=(5^11)^3×(11^11)^3

9^123=(9^41)^3=(9^11×9^30)^3=(9^11)^3×(9^30)^3=(9^11)^3×[(9^2)^15]^3=(9^11)^3×(81^15)^3

(5^11)^3 < (9^11)^3

(11^11)^3 < (81^15)^3

Deci 55^33 < 9^123