Question

chứng minh rằng 24^54.54^24.2^10 chia hết cho 72^63

Answer 1

Ta có:

\(24^{54}.54^{24}.2^{10}=\left(2^3.3\right)^{54}.\left(3^3.2\right)^{24}.2^{10}\)

\(=\left(2^3\right)^{54}.3^{54}.\left(3^3\right)^{24}.2^{24}.2^{10}\)

\(=2^{162}.2^{24}.2^{10}.3^{54}.3^{72}\)

\(=2^{196}.3^{126}\)

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 \(2^{196}.3^{126}\) chia hết cho \(2^{189}.3^{126}\)

Nên: \(24^{54}.54^{24}.2^{10}\) chia hết cho \(72^{63}\)

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Chúc bạn học tốt :)