Question

Answer 1

\(81^7-27^9-9^{13}\)

\(=3^{28}-3^{27}-3^{26}\)

\(=3^{26}\cdot5⋮9\)

Answer 2

\(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}=3^{28}-3^{27}-3^{26}=3^{26}\left(3^2-3-1\right)=3^{24}\left(3^4-3^3-3^2\right)=3^{24}.45⋮45\)

Answer 3

Ta có:

\(81^7-27^9-9^{13}\\ =\left(3^4\right)^7-\left(3^3\right)^3-\left(3^2\right)^{13}\\ =3^{28}-3^{27}-3^{26}\\ =3^{26}.\left(3^2-3-1\right)=3^{26}.5=3^{24}.3^2.5=3^{24}.45\)

Mà 45 ⋮ 45 nên \(3^{24}.45⋮45\)

\(\Rightarrow81^7-27^9-9^{13}⋮45\left(đcpcm\right)\)