Question

so sánh:

\(444^{333}và333^{444}\)

Answer 1

Ta có :

444³³³=444^3.111=(444³)¹¹¹=87528384¹¹¹

333⁴⁴⁴=333^4.111=(333⁴)¹¹¹=12296370321¹¹¹

Vì 12296370321¹¹¹>87528384¹¹¹ nên 333⁴⁴⁴>444³³³

Answer 2

Ta có :

\(444^{333}=4^{333}.111^{333}\)

\(333^{444}=3^{444}.111^{444}\)

Vì \(111^{444}>111^{333}\) \(\left(1\right)\)

Mà \(4^{333}=\left(4^3\right)^{111}=64^{111}\) \(\left(2\right)\)

\(3^{444}=\left(3^4\right)^{111}=81^{111}\) \(\left(3\right)\)

Từ \(\left(1\right);\left(2\right);\left(3\right)\Rightarrow444^{333}< 333^{444}\)