A= 444 ^555=(444)^(5.111)=(444^5)^111
B=555^444=(555)^(4.111)=(555^4)^111
Ta so sánh 444^5 và 555^4
+) 444^5 =(4.111)^5=(4^5).(111^5)
=1024.(111^5) (1)
+) 555^4=(5.111)^4=(5^4).(111^4)
=625.(111^4) (2)
Từ (1);(2), ta có 444^5>555^4
=> (444^5)^111>(555^4)^111
=> A>B
Chúc bạn học tốt hi
Bạn tham khảo :
Theo đề bài ta có :
$A = 444^{555} = 444^{5.111} = 444^5 . 444^{111}$
$B = 555^{444} = 555^{4.111} = 555^5 . 555^{111}$
Ta có : (So sánh cái bé nha )
$444^5 = (4.111)^5 = 4^5 . 111^5 = 1024. 111^5$
$555^4 = (5.111)^4 = 5^4 . 111^4 = 625.111^4$
Vì $1024>625$ ⇒ $1024 . 111^5 > 625.111^4$
⇒ $A > B$
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