\(3^{203}=3^{200}.3^3=9^{100}.27\)
\(2^{302}=2^{300}.2^2=8^{100}.4\)
Vì \(9^{100}>8^{100}\); \(27>4\)\(\Rightarrow3^{203}>2^{302}\)
\(3^{203}>3^{202}=\left(3^2\right)^{101}=9^{101}\)
\(2^{302}< 2^{303}=\left(2^3\right)^{101}=8^{101}\)
\(\Rightarrow2^{302}< 8^{101}< 9^{101}< 3^{203}\)
Ta có: 3203=3200.33=(32)100.27=9100.27
2302=2300.22=(23)100.4=8100.4
Vì 9100>8100 và 27>4 nên 9100.27>8100.4
hay 3203>2302
Vậy 3203>2302.
