Question

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

Answer 1

\(24^{54}.54^{24}.2^{10}=3^{54}.2^{162}.2^{24}.3^{72}.2^{10}=3^{126}.2^{196}\)

ta có: \(72^{63}=9^{63}.8^{63}=\left(3^2\right)^{63}.\left(2^3\right)^{63}=3^{72}.2^{108}\)

ta có: \(\frac{3^{126}.2^{196}}{3^{72}.2^{108}}=3^{54}.2^{88}\)

suy ra \(3^{126}.2^{196}\) chia hết cho \(3^{72}.2^{108}\)

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