a)
`99^20 = ( 99^2 )^10 = ( 99 . 99 ) ^10 < ( 99 . 101 ) ^10 = 9990^10`
Vậy `9^20 = 9999^10`
b)
Ta có:$27^{25}$ =$(3^{3}) ^{25}$ =$3^{3.25}$ =$3^{75}$
$32^{15}$ =$(2^{5}) ^{15}$ =$2^{5.15}$ =$2^{75}$
Vì $2^{75}$ <$3^{75}$ ⇒$32^{15}$ <$27^{25}$
c) Ta có:$2^{84}$ =$2^{12.7}$ =$(2^{12} )^{7}$ =$4096^{7}$
$5^{35}$ =$5^{5.7}$ =$(5^{5}) ^{7}$ =$3125^{7}$
Vì $3125^{7}$ <$4096^{7}$ ⇒$5^{35}$ <$2^{84}$