\(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)\(=3^{28}-3^{27}-3^{26}=3^{26}\times\left(3^2-3-1\right)=3^{26}\times5\div3^4\times5\)
Nguyễn huy hoàng ơi, bn giải thích cho mk: 326x5:34 x5 vs....
Ta có :
\(81^7-27^9-9^{13}\)=\(\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)=\(3^{28}-3^{27}-3^{26}\)=\(3^{26}\left(3^2-3-1\right)=3^{26}.5=\left(3^4\right)^{22}.5\)
=\(81^{22}.5\)
Ta có 405= 81.5
mà 81^7-27^9-9^13 có thừa số 81 và 5 nên 81^7-27^9-9^13\(⋮\)405
\(81^7-27^9-9^{13}\)
\(=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)
\(=3^{28}-3^{27}-3^{26}\)
\(=\left(3^{26}.3^2\right)-\left(3^{26}.3^1\right)-\left(3^{26}.1\right)\)
\(=3^{26}.\left(3^2-3^1-1\right)\)
\(=3^{26}.\left(9-3-1\right)\)
\(=3^{22}.\left(3^4.5\right)\)
\(=3^{22}.405⋮405\)
\(\Rightarrow\)\(81^7-27^9-9^{13}⋮405\left(đpcm\right)\)
Rất vui vì giúp đc bạn !!!