99⁸⁸<88⁹⁹

99⁸⁸<88⁹⁹

3270 nha em, k đi rồi chj k lại

Kết quả là: 3270

1.M = 1992 . 19911991 - 1991 . 1992

M = 1992 . 1991 . 10001 - 1991 . 1992

M = 10001

Mình đã kiểm tra: Sai rồi bạn nha

Bg

Ta có: \(M=\frac{-2020}{55555^{66666}}\)và \(N=\frac{2020}{-66666^{55555}.11111^{11111}}\)

Xét \(M=\frac{-2020}{55555^{66666}}\):

=> \(M=\frac{-2020}{\left(11111.5\right)^{11111.6}}\)

=> \(M=\frac{-2020}{11111^{11111.6}.5^{11111.6}}\)

=> \(M=\frac{-2020}{11111^{11111.6}.5^{6^{11111}}}\)

=> \(M=\frac{-2020}{11111^{11111.6}.15625^{11111}}\)

Xét \(N=\frac{2020}{-66666^{55555}.11111^{11111}}\):

=> \(N=\frac{-2020}{\left(11111.6\right)^{11111.5}.11111^{11111}}\)

=> \(N=\frac{-2020}{11111^{11111.5}.6^{11111.5}.11111^{11111}}\)

=> \(N=\frac{-2020}{11111^{11111.5}.11111^{11111}.6^{11111.5}}\)

=> \(N=\frac{-2020}{11111^{11111.5+}^{11111}.6^{11111.5}}\)

=> \(N=\frac{-2020}{11111^{11111.6}.6^{11111.5}}\)

=> \(N=\frac{-2020}{11111^{11111.6}.7776^{11111}}\)

Vì 7776¹¹¹¹¹ < 15625¹¹¹¹¹ nên \(M=\frac{-2020}{11111^{11111.6}.15625^{11111}}\)> \(N=\frac{-2020}{11111^{11111.6}.7776^{11111}}\)

Vậy M > N

Cảm ơn a ạ!

Ta có:
\(222^{777}=111^{777}\cdot2^{777}\)            \(\left(1\right)\)
\(777^{222}=111^{222}.7^{222}\)              \(\left(2\right)\)
Ta lại có:
\(2^{777}=\left(2^7\right)^{111}=128^{111}\)         \(\left(3\right)\)
\(7^{222}=\left(7^2\right)^{111}=49^{111}\)           \(\left(4\right)\)
Từ \(\left(1\right),\left(2\right),\left(3\right)\) và \(\left(4\right)\)
\(\Rightarrow222^{777}>777^{222}\)

Ta có: 777³³³ = 777^(3.111) = (₇₇₇3)¹¹¹ = 2331¹¹¹

          333⁷⁷⁷ = 333^(7.111) = (₃₃₃7)¹¹¹ = 2331¹¹¹

=> 2331 = 2331 mà 2331¹¹¹ = 2331¹¹¹ hay 777³³³ = 333⁷⁷⁷

222^777 = (2 . 111) ^777 = 2^777 . 111^777 
= (2^7)^111 . (111^7)^111 

777^222. = (7 . 111)^222 = 7^222 . 111^222 
= (7^2)^111 . (111^2)^111 

So sánh ta thấy: 

2^7 > 7^2 
111^7 > 111^2 

==> (2^7)^111 . (111^7)^111 > (7^2)^111 . (111^2)^111 
==> 222^777 > 777^222 

Ta có : 222^777=(2.111)^7.111=128^111.(111^7)^111

            777^222=(7.111)^2.111=49^111.(111^2)^111

Vì 128^111>49^111

     (111^7)^111>(111^2)^111

=>222^777>777^222