Question

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

Answer 1

`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