Tham khảo
`a)` Có:`125^{31}=(5^3)^{21}=5^{63}`
`25^{47}=(5^2)^{47}=5^{94}`
Vì `5^{63}<5^{94}⇒125^{31}<25^{47}`
`b) A=1+2^1+2^2+...+2^{100}`
`⇒2A=2^1+2^2+...+2^{101}`
`⇒2A-A=2^1+2^2+...+2^{101}-(1+2^1+2^2+...+2^{100})`
`⇒A=2^{101}-1`
Vì `2^{101}-1<2^{101}`
`⇒A<B`
`c) C=1990^{10}+1990^9=1990^9×(1990+1)=1990^9×1991`
`D=1991^{10}=1991^9×1991`
Vì `1990^9×1991<1991^9×1991`
`⇒C<D`