\(81^7-27^9-9^{13}=3^{4.7}-3^{3.9}-3^{2.13}=3^{28}-3^{27}-3^{26}\)
\(=3^{26}\left(3^2-3-1\right)=3^{26}.5=3^{22}.3^4.5=3^{22}.81.5=405.3^{22}\)
Chia hết cho 405 => ĐPCM
405=3^4.5=81.5
27^9=27^8.27=3^24.27=81^6.27
9^13=9^12.9=8^6.9
mà 81^7-81^6.27-81^6.9=81^6.(81-27-9)=81^6.45 chia hết cho 81 và 5
Vậy ....