Question

Câu 1: So sánh: 222⁵⁵⁵ và 555²²²

Answer 1

222⁵⁵⁵ = ( 2.111 )^5.111 = 2^5.111.111^5.111 

555²²² = ( 5.111 )^2.111 = 5^2.111 .111^2.111

Vì 2⁵ > 5² ( 32 > 25 ) và 111⁵ > 111² ( 5 > 2 ) nên 2^5.111.111^5.111 > 5^2.111 .111^2.111

hay 222⁵⁵⁵ > 555²²²

Answer 2

\(\frac{222^{555}}{555^{222}}=\frac{\left(2.111\right)^{\left(5.111\right)}}{\left(5.111\right)^{\left(2.111\right)}}=111^{\left(111\left(5-2\right)\right)}.\left(\frac{2^5}{5^2}\right)^{111}=111^{333}.\left(\frac{32}{25}\right)^{1111}>1\)

\(222^{555}>555^{222}\)