Answer:
[tex]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[/tex]
[tex]3^{27}\cdot24[/tex] is divisible by 24, hence proving that [tex]27^{10}-9^{14}[/tex] is divisibe by 24
