Ta thấy:

\(11^{1979}< 11^{1980}\)

\(11^{1980}=\left(11^3\right)^{660}=1331^{660}\)

Và:

\(37^{1320}=\left(37^2\right)^{660}=1369^{660}\)

Mà: \(1331^{660}< 1369^{660}\)

\(\Rightarrow11^{1979}< 37^{1320}\)

11^1979 và 37^1320 

11^1979 < 12.1979 = (3.2.2)^1979 = 2^1979.6^1979 
37^1320 > 36^1320 = (6^2)^1320 = 6^2640 = 6^661.6^1979 

Ta thấy 

11¹⁹⁷⁹<11¹⁹⁸⁰ = 11^3.660 = (11³)⁶⁶⁰ = 1331⁶⁶⁰

37¹³²⁰ = 37^2.660 = (37²)⁶⁶⁰ = 1369⁶⁶⁰ > 1331⁶⁶⁰

=> 37 ¹³²⁰>11¹⁹⁷⁹

< khó kieens lik e quá chỉ thiếu có 2 cáu huhu

Ta có:

\(11^{1979}< 11^{1980}=\left(11^3\right)^{660}=1331^{660}\)

\(37^{1320}=\left(32^2\right)^{660}=1369^{660}\)

Mà: \(1369^{660}>1331^{660}\)

\(\Rightarrow\)\(11^{1979}< 37^{1320}\)

Lời giải:
$1990^{10}+1990^9=1990^9(1990+1)=1991.1990^9< 1991.1991^9=1991^{10}$

-----------------------

$10^{10}=(10^2)^5=100^5=(2.50)^5=2^5.50^5=32.50^5< 48.50^5$

------------------------

$11^{1979}< 11^{1980}=(11^3)^{660}=1331^{660}$
$37^{1320}=(37^2)^{660}=1369^{660}> 1331^{660}$

$\Rightarrow 11^{1979}< 37^{1320}$

\(^{11^{1979}}

11¹⁹⁷⁹ < 37¹³²⁰

11^1979 < 12.1979 = (3.2.2)^1979 = 2^1979.6^1979 
37^1320 > 36^1320 = (6^2)^1320 = 6^2640 = 6^661.6^1979