\(2^{54}.54^{24}.2^{10}\)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)
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