Question

so sánh \(333^{444}\)và\(444^{333}\)

Answer 1

Ta có :  333⁴⁴⁴ = (111.3)⁴⁴⁴ = 111⁴⁴⁴.3⁴⁴⁴

            444³³³ = (111.4)³³³ = 111³³³.4³³³

Tách : 3⁴⁴⁴ = 3^4.111 = 81¹¹¹

         4³³³ = 4^3.111 = 64¹¹¹

Mà 111⁴⁴⁴ > 111³³³ (1)

      81¹¹¹ > 64¹¹¹ hay 3⁴⁴⁴ > 4³³³ (2)

Từ (1) và (2) ta có : 3⁴⁴⁴ > 4³³³

Answer 2

\(333^{444}=444^{333}\)

Answer 3

Ta có:

333⁴⁴⁴=3⁴⁴⁴.111⁴⁴⁴=(3⁴)¹¹¹.111⁴⁴⁴=81¹¹¹.111⁴⁴⁴

444³³³=4³³³.111³³³=(4³)¹¹¹.111³³³=64¹¹¹.111³³³

Từ \(\begin{cases}81^{111}>64^{111}\\111^{444}>111^{333}\end{cases}\Rightarrow81^{111}.111^{444}>64^{111}.111^{333}}\)

=>333⁴⁴⁴>444³³³