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

\(37^{1320}=\left(37^2\right)^{600}=1369^{600}\)

\(1369^{660}>1331^{660}\Rightarrow11^{1979}<37^{1320}\)

b) \(1990^{10}+1990^9=1990^9\left(1990+1\right)=1990^9.1991<1991^9.1991\)

\(\Rightarrow1990^{10}+1990^9<1991^{10}\)

Vậy \(1990^{10}+1990^9<1991^{10}\)

a)11¹⁹⁷⁹<37¹³²⁰

b)1990¹⁰+1990⁹<1991¹⁰

1; 11¹⁹⁷⁹ > 37¹³²⁰

2; 1990¹⁰ + 1990⁹ > 1991¹⁰

Ta có :

1990^10 + 1990^9 = 1990.1990^9 + 1990^9 = 1991^9 < 1991^10 
=> (1990^10 + 1990^9) < 1991^10 

quá dễ

Lời giải:

$A=1990^{10}+1990^9=1990^9(1990+1)=1990^9.1991< 1991^9.1991=1991^{10}$

Hay $A< B$

\(1990^{10}>1990^9\left(1\right)\)

Ta có  \(1991^1=1990^1+1990^0\)

mà \(\)\(1990^1+1990^0< 1990^9\left(1990>1\right)\)

\(\Rightarrow1990^9>1991^1\left(2\right)\)

\(\left(1\right),\left(2\right)\Rightarrow1991^1< 1990^9< 1990^{10}\)