a) Ta có: \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\Rightarrow99^{20}< 9999^{10}\)
b) Ta có: \(2^{31}=\left(2\frac{31}{21}\right)^{21}=2,7822^{21}< 3^{21}\Rightarrow2^{31}< 3^{21}\)
c) Ta có: \(3^{30}=\left(3^3\right)^{10}=27^{10}\)
\(2^{30}=\left(2^3\right)^{10}=8^{10}\)
\(4^{30}=\left(4^3\right)^{10}=64^{10}\)
Lại có: \(3.24^{10}=2.24^{10}+24^{10}\Rightarrow24^{10}< 27^{10}\left(1\right)\)
\(2.24^{10}< 48^{10}< 64^{10}\left(2\right)\)
Từ 1,2 => \(24^{10}+2.24^{10}< 27^{10}+64^{10}\Rightarrow3.24^{10}< 8^{10}+27^{10}+64^{10}\)
\(\Rightarrow3.24^{10}< 3^{30}+2^{30}+4^{30}\)
