Ta có: \(8^7-2^{18}\)

\(=\left(2^3\right)^7-2^{18}\)

\(=2^{21}-2^{18}\)

\(=2^{18}.\left(2^3-1\right)\)

\(=2^{18}.7\)

\(=2^{17}.2.7\)

\(=2^{17}.14\)

Vì \(14⋮14\) nên \(2^7.14⋮14.\)

=> \(8^7-2^{18}⋮14\left(đpcm\right).\)

Chúc bạn học tốt!

*Ta có : 8⁷ - 2¹⁸

= (2³)⁷ - 2¹⁸

= 2²¹ - 2¹⁸

= 2¹⁸ . ( 8 - 1)

= 2¹⁷ . 2 . 7

= 2¹⁷ . 14 \(⋮\) 14

*Hay : 8⁷ - 2¹⁸ \(⋮\) 14. (đpcm)

*Tick nhé bạn!

Ta có: 8⁷-2¹⁸=1835008

- 1835008 chia hết cho 14 <=> 1835008 chia hết cho 7 và 2

mà 1835008: 7=262144

     1835008: 2=917504

=> 8⁷-2¹⁸ chia hết cho 14.

\(8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{17}\left(2^4-2\right)=2^{17}.14⋮14\)

\(8^7-2^{18}\)

\(=2^{21}-2^{18}\)

\(=2^{18}\left(2^3-1\right)=2^{18}.7\)

\(=2^{17}.14⋮14\)

8^7 - 2^18 

=(2^3)^7-2^18

=2^21-2^18

=2^18.2^3-2^18.1

=2^18.8-2^18.1

=2^18.(8-1)

=2^18.7

=2^17.2^1.7

=2^17.2.7

=2^17.(2.7)

=2^17.14 chia hết cho 14

Ta có:

\(8^7-2^{18}=8^7-\left(2^3\right)^6=8^7-8^6=8^5.\left(8^2-8\right)=8^5.56⋮14\)

\(\Rightarrow8^7-2^{18}⋮14\left(đpcm\right)\)

\(8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{18}.2^3-2^{18}=2^{18}\left(2^3-1\right)=2^{18}.7=2^{17}.2.7=2^{17}.14⋮14\)

Vây....................

1] chứng minh rằng ab - ab chia hết cho 9

Ta có:ab-ab=0\(⋮\)9

2] chứng minh rằng 7 mũ 8+ 7 mũ 7 - 7 mũ 6chia  hết cho 55

Ta có:7⁸+7⁷-7⁶=7⁶.(7²+7-1)=7⁶.55\(⋮\)5

\(\overline{ab}-\overline{ba}\)

\(=\left(10a+b\right)-\left(10b+a\right)\)

\(=9a-9b\)

\(=9\left(a-b\right)⋮9\)

\(7^8+7^7-7^6\)

\(=7^6\cdot\left(7^2+7-1\right)\)

\(=7^6\cdot\left(49+7-1\right)\)

\(=7^6\cdot\left(56-1\right)\)

\(=7^6\cdot55⋮55\)

câu b,c có nhầm không bạn nhỉ 

A=2+2²+2³+...+2²⁰¹⁶

= (2+2²+2³)+(2⁴+2⁵+2⁶)+...+(2²⁰¹⁴+2²⁰¹⁵+2²⁰¹⁶)

= 2.(1+2+2²)+2⁴.(1+2+2²)+...+2²⁰⁰⁴.(1+2+2²)

= 2.7+2⁴.7+...+2²⁰¹⁴.7

= 7.(2+2⁴+...+2²⁰¹⁴) chia het cho 7

=> dpcm
 

\(8^7-2^{18}=\left(2^3\right)^7-2^{18}=2^{21}-2^{18}=2^{18}\left(2^3-1\right)=2^{17}.2.7=2^{17}.14⋮14\left(đpcm\right)\)