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Ta có:
\(24^{54}.54^{24}.2^{10}=\left(2^3.3\right)^{54}.\left(3^3.2\right)^{24}.2^{10}\)
\(=\left(2^3\right)^{54}.\left(3^3.2\right)^{24}.2^{10}\)
\(=2^{162}.3^{54}.3^{72}.2^{24}.2^{10}\)
\(=2^{196}.3^{126}\) (1)
Lại có:
\(72^{63}=\left(2^3.3^2\right)^{63}=2^{189}.3^{126}\)(2)
Từ (1) và (2) ⇒ \(24^{54}.54^{24}.2^{10}⋮72^{63}\)
a, \(81^7-27^9-9^{13}\)
\(=3^{28}-3^{27}-3^{26}\)
\(=3^{22}\left(3^6-3^5-3^4\right)\)
\(=3^{22}\times405⋮405\)
\(24^{54}.54^{24}.2^{10}\)
\(=\left(2^3.3\right)^{54}.\left(3^3.2\right)^{24}.2^{10}\)
\(=\left(2^3\right)^{54}.3^{54}.\left(3^3\right)^{24}.2^{24}.2^{10}\)
\(=2^{162}.3^{54}.3^{72}.2^{24}.2^{10}\)
\(=2^{196}.3^{126}\)
Lại có :
\(72^{63}=\left(2^3.3^2\right)^{63}\)
\(=\left(2^3\right)^{63}.\left(3^2\right)^{63}\)
\(=2^{189}.3^{126}\)
Vì \(2^{196}.3^{126}⋮2^{189}.3^{126}\Leftrightarrowđpcm\)
a. 87 - 218 = 221 - 218 = 217 ( 24 - 2) = 217 ( 16-2) = 217 * 14 chia het cho 14
b. 55 - 54 + 53 = 53 ( 52 - 5 + 1) = 53 * 21 chia het cho 7
con nhung bai lai ban tu giai nhe , con neu thac mac hoi ban
\(2^{54}.54^{24}.2^{10}\)chia hết \(72^{63} \)
\(2^{54}.54^{24}.2^{10}\)=\((2^3.3)^{54}.(3^3.2)^{24}.2^{10}\)
=\((2^3)^{54}.3^{54}.(3^3)^{24}.2^{24}2^{10}\)
= \(2^{162}.2^{24}.2^{10}.3^{54}.3^{72} \)
=\(2^{196}.3^{126}\)
\(72^{63} \)=\((2^3.3^2)^{63}\)
=\((2^3)^{63}.(3^2)^{63}=2^{189}.3^{126}\)
Vì \(2^{196}.3^{126}\)chia hết \(2^{189}.3^{126}\)\(24^{54}.54^{24}.2^{10}\)
\(\Rightarrow \)\(24^{54}.54^{24}.2^{10}\)chia hết \(72^{63} \)(dpcm)