Question

So sánh:

555²⁰ và 222⁵⁰

Answer 1

Ta có:

555²⁰ = (5.111)²⁰ = 5²⁰.111²⁰ = (5²)¹⁰.111²⁰ = 25¹⁰.111²⁰

222⁵⁰ = (2.111)⁵⁰ = 2⁵⁰.111⁵⁰ = (2⁵)¹⁰.111⁵⁰ = 32¹⁰.111⁵⁰

Vì 25¹⁰.111²⁰ < 32¹⁰.111⁵⁰

=> 555²⁰ < 222⁵⁰

Answer 2

Ta có: 555^20 = (5 . 111)^20 = 5^20 . 111^20 = (5^2)^10 . 111^20 = 25^10 . 111^20

222^50 = (2 . 111)^50 = 2^50 . 111^50 = (2^5)^10 . 111^50 = 32^10 . 111^50

Vì 25^10 < 32^10 và 111^20 < 111^50 nên 25^10 . 111^20 < 32^10 . 111^50

Vậy 555^20 < 222^50.