$\text{a) $5^{23}$<6.$5^{22}$}$
$\text{Vì 6.$5^{22}$=6.$5^{22}$=5.$5^{22}$+$5^{22}$=$5^{23}$+$5^{22}$}$
$\text{Mà $5^{23}$<$5^{23}$+$5^{22}$}$
$\text{Nên $5^{23}$<6.$5^{22}$}$
$\text{b) $2^{16}$>7.$2^{13}$}$
Vì $2^{16}$=$2^{13}$.$2^{3}$=$2^{13}$.8=$2^{13}$.7+$2^{13}$
$\text{Mà $2^{13}$.7+$2^{13}$>7.$2^{13}$}$
$\text{Nên $2^{16}$>7.$2^{13}$}$
$\text{c) $21^{15}$<$27^{5}$.$49^{8}$}$
$\text{Vì $21^{15}$=$3^{15}$.$7^{15}$}$
$27^{5}$=$3^{15}$
$49^{8}$=$7^{16}$
$\text{Mà $3^{15}$.$7^{15}$<$3^{15}$.$7^{16}$}$
$\text{Nên $21^{15}$<$27^{5}$.$49^{8}$}$
