a) Ta có: $3^{500}$ = $3^{5.100}$ = $(3^{5})^{100}$ = $243^{100}$
$7^{300}$ = $7^{3.100}$ = $(7^{3})^{100}$ = $343^{100}$
Vì $243^{100}$ < $343^{100}$ ⇒ $3^{500}$ < $7^{300}$
b) Ta có: $27^{5}$ = $(3^{3})^{5}$ = $3^{3.5}$ = $3^{15}$
$243^{3}$ = $(3^{5})^{3}$ = $3^{5.3}$ = $3^{15}$
Vì $3^{15}$ = $3^{15}$ ⇒ $27^{5}$ = $243^{3}$