2454.5424.210 = (23.3)54.(2.33)24.210 = 2162.354.224.372.210 = 2196.3126 = 27(2189.3126) = 27.[(23)63.(32)63] = 27.(863.963) = 27.7263 chia hết cho 7263
Tính: (1 - 1/4 ) . (1 - 1/9) . (1 - 1/16) ... (1 - 1/81) . (1 - 1/100)
-Ta có:
+\(72^{63}=\left(2^3\cdot3^2\right)^{63}=\left(2^3\right)^{63}\cdot\left(3^2\right)^{63}=2^{189}\cdot3^{126}\)
+\(24^{54}\cdot54^{24}\cdot2^{10}\)
=\(\left(2^3\cdot3\right)^{54}\cdot\left(2\cdot3^3\right)^{24}\cdot2^{10}\)
=\(2^{162}\cdot3^{54}\cdot2^{24}\cdot3^{72}\cdot2^{10}\)
=\(2^{196}\cdot3^{126}\)
=\(2^7\cdot2^{189}\cdot3^{126}\)
Vì \(2^7\cdot2^{189}\cdot3^{126}⋮2^{189}\cdot3^{126}\)
\(\Rightarrow24^{54}\cdot54^{24}\cdot2^{10}⋮2^{63}\)