\(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}=3^{28}-3^{27}-3^{26}=3^{26}.\left(3^2-3-1\right)\)
\(=3^{26}.\left(9-3-1\right)=3^{26}.5=3^{24}.3^2.5=3^{24}.9.5=3^{24}.45\) chia hết cho 45
=> hiệu trên chia hết cho 45
=> đpcm