`99^20 và 9999^10`
`a) 99^20=99^(2.10)=9801^10`
Vì:`9801^10<9999^10`
`⇒99^20<9999^10`
b)
$10^{10}$ $\textrm{và}$ $48.50^{5}$
$10^{10} = (10^{2})^{5} = 100^{5} = (50.2)^{5} = 50^{5} . 2^{5}$ = $50^{5}. 32$
$\textrm{Vì 32 < 48 và}$ $50^{5} = 50^{5}$
$⇒ 50^{5} . 32 < 50^{5} = 50^{5}$ $\textrm{hay}$ $(10^{2})^{5} < 48.50^{5}$
$\textrm{Vậy}$ $10^{10} < 48.50^{5}$
c)
`107^50= (107^2)^25= 11449^25`
`73^75= (73^3)^25= 389017^25`
vì `11449 < 389017` nên `11449^25 < 389017^25`
⇒ `107^50 < 73^75`
