Hướng dẫn trả lời:
a) Ta có:
$\text{$2^{225}$ = $(2^{3})^{75}$ = $8^{75}$.}$
$\text{$3^{150}$ = $(3^{2})^{75}$ = $9^{75}$.}$
$\text{Vì $8^{75}$ < $9^{75}$ nên $2^{225}$ < $3^{150}$.}$
$\text{Vậy $2^{225}$ < $3^{150}$.}$
b) Ta có:
$\text{$2^{91}$ > $2^{90}$= $(2^{5})^{18}$ = $32^{18}$.}$
$\text{$5^{35}$ < $5^{36}$ = $(5^{2})^{18}$ = $25^{18}$.}$
$\text{Vì 32 > 25 nên $32^{18}$ > $25^{18}$.}$
$\text{→ $2^{91}$ > $32^{18}$ > $5^{35}$ > $25^{18}$.}$
$\text{Vậy $2^{91}$ > $5^{35}$.}$
c) Ta có:
$\text{$99^{20}$ = $(99^{2})^{10}$ = $9801^{10}$.}$
$\text{Vì $9801^{10}$ < $9999^{10}$ nên $99^{20}$ < $9999^{10}$.}$
$\text{Vậy $99^{20}$ < $9999^{10}$.}$
