\(24^{54}.54^{24}.2^{10}=\left(2^3.3\right)^{54}.\left(2.3^3\right)^{24}.2^{10}=2^{162}.3^{54}.2^{24}.3^{72}.2^{10}=2^{196}.3^{126}\)

\(72^{63}=\left(2^3.3^2\right)^{63}=2^{189}.3^{126}\)

Mà \(2^{196}.3^{126}⋮2^{189}.3^{126}\Rightarrow24^{54}.54^{24}.2^{10}⋮72^{63}\)

XIN NỖI TOÁN 6

24^54 * 54^24 * 2^10 = (3 * 2^3)^54 * (2 * 3^3)^24 * 2^10 
= 3^126 * 2^196(1)
72^63 = (2^3 * 3^2) ^63 = 2^189 * 3^126(2)

từ (1) và (2)=>24^54 * 54^24 * 2^10 chia hết 72^63

a) \(7^6+7^5-7^4\)chia hết cho 11

\(=7^4\left(7^2+7-1\right)\)

 \(=7^4.55=7^4.5.11\)chia hết cho 11

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

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

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

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

 \(=2^{196}.3^{126}\)

 \(72^{63}=\left(2^3.3^2\right)^{63}\)

 \(=\left(2^3\right)^{63}.\left(3^2\right)^{63}=2^{189}.3^{126}\)

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

\(\Rightarrow24^{54}.54^{24}.2^{10}\)chia hết cho\(72^{63}\)

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

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 \(72^{63}\)