81^7-27^9-9^{13}

=(9^2)^7 - (3\times9)^9-9^{13}

=9^{14} - 3\cdot 3^8\cdot 9^9-9^{13}

=9^{14} - 3\cdot 9^4\cdot 9^9-9^{13}

=9^{14} - 3\cdot 9^{13}-9^{13}

=9^{14} - 4\cdot 9^{13}

=9^{13}(9-4)

=5\cdot9^{13}

Therefore

81^7-27^9-9^{13} is divisible by 45