a) $3^{300}$ = ($3^{3}$)$^{100}$ = $27^{100}$
$2^{500}$ = ($2^{5}$)$^{100}$ = $32^{100}$
Vì: $27^{100}$ < $32^{100}$ ⇒$3^{300}$ < $2^{500}$.
b) $12^{45}$ = $12^{3.15}$ = ($12^{3}$)$^{15}$ = $1728^{15}$
Vì: $1728^{15}$ > $625^{15}$ ⇒$12^{45}$ > $625^{15}$