\(8^7-2^{18}=\left(2^3\right)^7-2^{18}\)
\(=2^{21}-2^{18}\)
\(=2^{17}.\left(2^4-2\right)\)
\(=2^{17}.\left(16-2\right)\)
\(=2^{17}.14\)
Ta có: \(14⋮14\)
\(\Rightarrow2^{17}.14⋮14\)
\(\Rightarrow8^7-2^{18}⋮14\)
đpcm
Ta có : \(8^7-2^{18}\)
\(=(2^3)^7-2^{18}\)
\(=2^{21}-2^{18}\)
\(=2^{18}\cdot2^3-2^{18}\)
\(=2^{18}\cdot7⋮7\)
Mà \(2^{18}⋮2\Rightarrow2^{18}\cdot7⋮2\)
Mà \((2;7)=1\)
\(\Rightarrow2^{18}\cdot7⋮14\)
Vậy : \(8^7-2^{18}⋮14(đpcm)\)
Chúc bạn học tốt
\(8^7-2^{18}\)
\(=\left(2^3\right)^7-2^{18}\)
\(=2^{21}-2^{18}\)
\(=2^{18}\left(8-1\right)=2^{17}.14⋮14\)
Ta có: \(8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{17}\left(2^4-2\right)=2^{17}\cdot\left(16-2\right)=2^{17}\cdot14\)
Ta thấy \(14⋮14\Leftrightarrow2^{17}\cdot14⋮14\)
\(\Leftrightarrow8^7-2^{18}⋮14\)
Vậy \(8^7-2^{18}⋮14\left(đpcm\right)\)