Ta có:
\(3^{21}=3.3^{20}=3.\left(3^2\right)^{10}=3.9^{10}\)
\(2^{31}=2.2^{30}=2.\left(2^3\right)^{10}=2.8^{10}\)
Vì \(3.9^{10}>2.8^{10}\) nên \(3^{21}>2^{31}\)
ta có :
\(3^{21}\) = 3.\(3^{20}\) = 3. \(9^{10}\)
\(2^{31}\) =2. \(2^{30}\) = 2.\(8^{10}\)
Vì 3.\(9^{10}\) > 2.\(8^{10}\) => \(3^{21}\) > \(2^{31}\)
Ta có: \(3^{21}=3\cdot3^{20}=3\cdot\left(3^2\right)^{10}=3\cdot9^{10}\)
\(2^{31}=2\cdot2^{30}=2\cdot\left(2^3\right)^{10}=2\cdot8^{10}\)
Ta thấy: \(2< 3;8^{10}< 9^{10}\)
\(\Rightarrow3\cdot9^{10}>2\cdot8^{10}\)
hay \(3^{21}>2^{31}\)
Vậy \(3^{21}>2^{31}\)
giúp em ạ