trả lời

555^2<222^555

chúc bn 

hc tốt

#)Giải :

Ta có : \(555^{222}=555^{2.111}=\left(111.5\right)^{2.111}=5^2.111^{111}=25.111^{111}\)

            \(222^{555}=222^{5.111}=\left(111.2\right)^{5.111}=2^5.111^{111}=32.111^{111}\)

Vì \(25< 32\Rightarrow25.111^{111}< 32.111^{111}\Rightarrow555^{222}< 222^{555}\)

trả lời 

555^222<222^555

chúc bn 

hc tốt

Nhầm:

So sánh 555²²² và 222⁵⁵⁵

555²²²=(555²)¹¹¹

222⁵⁵⁵=(222⁵)¹¹¹

Vì 555²²²-222⁵⁵⁵<0

Nên 555²²²<222⁵⁵⁵

So sánh 555²²² và 222⁵⁵⁵

555²²²=555^2.111=(111.5)^2.111=5².111¹¹¹=25.111¹¹¹

222⁵⁵⁵=222^5.111=(111.2)^5.111=2⁵.111¹¹¹=32.111¹¹¹

Vì 25.111¹¹¹<32.111¹¹¹

Nên 555²²²<222⁵⁵⁵

222^555=(222^5)^111 
555^222=(555^2)^111 
 222^5-555^2>0 
=> 222^555> 555^222  đây ko giống sao 

Theo đề ta có: 222⁵⁵⁵ và 555²²²

=> 222⁵⁵⁵ = (222⁵)¹¹¹

=> 555²²² = (555²)¹¹¹

=> 555²²² - 222⁵⁵⁵ < 0

=> 555^{222 <} 222⁵⁵⁵

ủng hộ nha!

222⁵⁵⁵ = (2.111)⁵⁵⁵ = 2⁵⁵⁵.111⁵⁵⁵ = (2⁵)¹¹¹.111⁵⁵⁵ = 32¹¹¹.111⁵⁵⁵

555²²² = (5.111)²²² = 5²²².111²²² = (5²)¹¹¹.111²²² = 25¹¹¹.111²²²

Vì 25 < 32 nên 25¹¹¹ < 32¹¹¹; 111²²² < 111⁵⁵⁵

=> 32¹¹¹.111⁵⁵⁵ > 25¹¹¹.111²²² => 222⁵⁵⁵ > 555²²²

ta có: 222⁵⁵⁵ = ( 2.111)⁵⁵⁵ = 2⁵⁵⁵.111⁵⁵⁵= (2⁵)¹¹¹.111⁵⁵⁵ = 32¹¹¹.111⁵⁵⁵

555²²²  = ( 5.111)²²² = 5²²².111²²² = ( 5²)¹¹¹.111²²² = 25¹¹¹.111²²²

mà 32¹¹¹> 25¹¹¹; 111⁵⁵⁵>111²²²

=> 32¹¹¹.111⁵⁵⁵>25¹¹¹.111²²²

=> 222⁵⁵⁵> 555²²²

Ta có:

222⁵⁵⁵ = 111⁵⁵⁵.2⁵⁵⁵ = 111²²².111³³³.(2⁵)¹¹¹ = 111²²².111³³³.32¹¹¹

555²²² = 111²²².5²²² = 111²²².(5²)¹¹¹ = 111²²².25¹¹¹

Do 111³³³.32¹¹¹ > 25¹¹¹

=> 111²²².111³³³.32¹¹¹ > 111²²².25¹¹¹

=> 222⁵⁵⁵ > 555²²²

222⁵⁵⁵=(222⁵)¹¹¹

555²²²=(555²)¹¹¹

Đến đây, ta chỉ cần so sánh 222⁵ và 555²

Ta có 222²>555 ( vì 222² nhiều chữ số hơn

Do đó (222²)²>555²

=>222⁴>555²

=>222⁵>555²

Vậy 222⁵⁵⁵>555²²²

\(222^{555}=\left(222^5\right)^{111}\)

\(555^{222}=\left(555^2\right)^{111}\)

mà \(222^5>555^2\Rightarrow222^{555}>555^{222}\)

Vậy \(222^{555}>555^{222}\)

Nhớ k cho mình nhé! Thank you!!!

222^555 > 555^222

k cho mk nha

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

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

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