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Prove that 27 to the 10th-9 to the 14th is divisible by 24
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Prove that 27 to the 10th-9 to the 14th is divisible by 24

User Luca Nicoletti
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5 votes

Answer:


27^(10)-9^(14)\\\\=(3^3)^(10)-(3^2)^(14)\\\\=3^(30)-3^(28)\\\\=3^((27+3))-3^((27+1))\\\\=3^(27) \cdot3^3-3^(27)\cdot3^1\\\\=3^(27)(3^3-3^1)\\\\=3^(27)(27-3)\\\\=3^(27)\cdot24


3^(27)\cdot24 is divisible by 24, hence proving that
27^(10)-9^(14) is divisibe by 24

User Goran Usljebrka
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