Ta có :
\(1990^{10}+1990^9=199^9\left(199.10^9\right)\)
\(1991^{10}>1990^{10}=199^{10}.10^{10}=199^9.199.10^{10}\)
Vì \(199^9\left(199.10^9\right)< 199^9.199.10^{10}=1991^{10}\)
\(\Rightarrow199^{10}+1990^9< 1991^{10}\)
199010 + 19909 = 9,744261891 x 1032
199110 = 9,788420103 x 1032
Vì 9,744261891 x 1032 < 9,788420103 x 1032
Nên 199010 + 19909 < 199110