333⁴⁴⁴=(3.111)^4.111=(81.111⁴)¹¹¹=(81.111.111³)¹¹¹

444³³³=(4.111)^3.111=(64.111³)¹¹¹

Vì (81.111.111³)¹¹¹>(64.111³)¹¹¹ nên 333⁴⁴⁴>444³³³

Ta có: 333⁴⁴⁴ = (3.111)⁴⁴⁴ = 3⁴⁴⁴.111⁴⁴⁴ = 81¹¹¹.111⁴⁴⁴

          444³³³ = (4.111)³³³ = 4³³³.111³³³= 64¹¹¹.111³³³

Vì 81¹¹¹ > 64¹¹¹, 111⁴⁴⁴ > 111³³³ nên 81¹¹¹ . 111⁴⁴⁴ > 64¹¹¹.111³³³

  Vậy 333⁴⁴⁴ < 444³³³

a)\(333^{444}=3^{444}.111^{444}=\left(3^4\right)^{111}.111^{444}=81^{111}.111^{444}\)

\(444^{333}=4^{333}.111^{333}=\left(4^3\right)^{111}.111^{333}=64^{111}.111^{333}\)

Từ \(\hept{\begin{cases}81^{111}>64^{111}\\111^{444}>111^{333}\end{cases}}\Rightarrow81^{111}.111^{444}>64^{111}.111^{333}\Rightarrow333^{444}>444^{333}\)

b)\(5^{300}=\left(5^2\right)^{150}=25^{150};4^{453}=\left(4^3\right)^{151}=64^{151}\)

Vì 25¹⁵⁰<64¹⁵¹ => 5³⁰⁰<4⁴⁵³

c)\(5^{217}>5^{216}=\left(5^3\right)^{72}=125^{72}>119^{72}\) => \(5^{217}>119^{72}\)

CẢM ƠN NHIỀU LẮM!

Anh em k mik nha mik cảm ơn nha^_^

5\(^{300}\)=25\(^{150}\)

3\(^{453}\)=27\(^{151}\)=27.27\(^{150}\)

vì 25\(^{150}\)<27.27\(^{150}\)

\(\Rightarrow\)5\(^{300}\)<3\(^{453}\)

31\(^{11}\)<32\(^{11}\)=(2\(^5\))\(^{11}\)=2\(^{55}\)

31\(^{11}\)<2\(^{55}\)

17\(^{14}\)>16\(^{14}\)=2\(^{56}\)

31\(^{11}\)<2\(^{55}\)<2\(^{56}\)<17\(^{14}\)

\(\Rightarrow\)31\(^{11}\)<17\(^{14}\)

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

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

ta có 3\(^{444}\)=81\(^{111}\)

4\(^{333}\)=64\(^{111}\)

\(\Rightarrow\)3\(^{444}\)>4\(^{333}\)(81\(^{111}\)>64\(^{111}\))

111\(^{444}\)>111\(^{333}\)

3\(^{444}\).111\(^{444}\)>4\(^{333}\).111\(^{333}\)

Vậy 333\(^{444}\)>444\(^{333}\)

nảy mình làm thiếu 1 câu bây giờ bù nhá

10³⁰= (10³)¹⁰= 1000¹⁰

2¹⁰⁰=(2¹⁰)¹⁰=1024¹⁰

1000<1024 =>1000¹⁰<1024¹⁰ nên 10³⁰<2¹⁰⁰