Ta có: 
\(\Rightarrow\)\(4^{555}>5^{444}\)

Ta co : 

3²⁰⁰ va 2³⁰⁰

3²⁰⁰=(3²)¹⁰⁰=9¹⁰⁰

2³⁰⁰=(2³)¹⁰⁰=8¹⁰⁰

Ma : 9¹⁰⁰>8¹⁰⁰

Vay suy ra 3²⁰⁰>2³⁰⁰

tu lm tiep nhe

\(5^{444}=\left(5^4\right)^{111}=625^{111}\)

\(4^{555}=\left(4^5\right)^{111}=1024^{111}\)

Vì \(625<1024\text{ nên }625^{111}<1024^{111}\)

Vậy \(5^{444}<4^{555}\).

444 mũ 555 =(4 nhân 111) mũ 555 = ((4^5 x 111)^111 x 111^444 
555 mũ 444 = (5 nhân 111) mũ 444 = (5^4)^111 x 111^444 
suy ra 444 mũ 555 > 555 mũ 444 
Phần D 10^30=(10^3)^10 
2^100 = (2^10)^10 
suy ra 10^30<2^100

Ta có:5⁴⁴⁴=(5⁴)¹¹¹=625¹¹¹

4⁵⁵⁵=(4⁵)¹¹¹=1024¹¹¹

Vì 1024¹¹¹>625¹¹¹ nên 4⁵⁵⁵>5⁴⁴⁴

444^5= (111^4)^5=11^20 

555^4= (111^5)^4=111^20 

=) 444^5=555^4

\(444^5=\left(444^{\frac{5}{4}}\right)^4\approx2038^4\)

vì:\(2038^4>555^4\Rightarrow444^5>555^4\)

Ta xét :

\(444^{555}=\left(444^5\right)^{111}=\left(111^5.4^5\right)^{111}=\left(111^5.1024\right)^{111}\)

\(555^{444}=\left(555^4\right)^{111}=\left(111^4.5^4\right)^{111}=\left(111^4.625\right)^{111}\)

Mà \(111^5.1024>111^4.625\)

\(\Rightarrow444^{555}>555^{444}\)

ta có: \(444^{555}=444^{\left(111\times5\right)}=\left(444^5\right)^{111}\)

\(555^{444}=555^{\left(111\times4\right)}=\left(555^4\right)^{111}\)

ta có:  \(444^5=\left(4\times111\right)^5=4^5\times111^5\)= \(1024\times111\times111^4\)

            \(555^4=\left(5\times111\right)^4=5^4\times111^4\) = \(625\times111^4\)

ta có: \(1024\times111\times111^4\) > \(625\times111^4\)

   \(\Rightarrow\)\(444^5>555^4\)

mình làm hơi tắt bạn tự hoàn thiện nha.

444⁵ > 555⁴ 

Tại sao vậy bạn ?

Ta có : 

\(444^5\)=   \(\left(111.4\right)^5\)=   \(111^5\).   \(4^5\)

\(555^4\)=   \(\left(111.5\right)^4\)=   \(111^4\).   \(5^4\)

Vì   \(111^5\).   \(4^5\)>   \(111^4\).   \(5^4\)

Vậy ..................................

\(2019^{2017}=\left(2019^{\frac{2017}{2018}}\right)^{2018}\approx2001,4^{2018}\)

Vì \(2001,4< 2017\Rightarrow2019^{2017}< 2017^{2018}\)

Ơ , nhưng mà ko dùng máy tính để làm bài mà .