1) \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\)
2) \(3^{21}=3^{20}\cdot3=9^{10}\cdot3\)
\(2^{31}=2^{30}\cdot2=8^{10}\cdot2\)
mà \(9^{10}\cdot3>8^{10}\cdot2\)=> tự viết tiếp
3) đợi chút
430 = (43)10 = 6410 > 4810 = ( 2 . 24 )10 = ( 210 ) . ( 2410 ) > 3 . 2410
=> 230 + 330 + 430 > 3 . 2410
.
*99^20=(90^2)^10=8100^10<9999^10
vậy 99^20<9999^10
*3^21=(3^2)10.3=9^10.3
2^31=(2^3)10.2=8^10.2
9^10.3>8^10.2
Vậy 3^21>2^31