Đáp án:
1. $31^{11}$ < $17^{14}$
2. $127^{23}$ < $513^{18}$
Giải thích các bước giải:
1. ta có: $31^{11}$ < $32^{11}$
mà $32^{11}$ = ($2^{5}$)$^{11}$ = $2^{55}$
vậy $31^{11}$ < $2^{55}$
$17^{14}$ > $16^{14}$
mà $16^{14}$ = ($2^{4}$)$^{14}$ = $2^{56}$
vậy $17^{11}$ > $2^{56}$
mà $2^{56}$ > $2^{55}$ ⇒ $31^{11}$ < $17^{14}$
2. ta có:
$127^{23}$ < $128^{23}$ = ($2^{7}$)$^{23}$ = $2^{161}$
$513^{18}$ > $512^{18}$ = ($2^{9}$)$^{18}$ = $2^{162}$
vậy $127^{23}$ < $513^{18}$
