Cmr: 1, 81^7 - 27^9 - 9^13 chia hết cho 15
2, 24^54.54^24.2^100 chia hết cho 72^63
1. $81^7-27^9-9^{13}$
$=(3^4)^7-(3^3)^9-(3^2)^{13}$
$=3^{28}-3^{27}-3^{26}$
$=3^{26}(3^2-3-1)$
$=3^{24}.3^2.5$
$=3^{24}.45 \ \vdots \ 45$
2. $24^{54}.54^{24}.2^{100}$
$=(3.2^3)^{54}.(2.3^3)^{24}.2^{100}$
$=3^{54}.2^{162}.2^{24}.3^{72}.2^{100}$
$=2^{286}.3^{126}$
$=2^{97}(2^{189}.3^{126})$
$=2^{97}.[(2^3)^{63}.(3^2)^{63}]$
$=2^{97}(8^{63}.9^{63})$
$=2^{97}.72^{63} \ \vdots \ 72^{63}$