7^86+7^85-7^84

=7^84.7^2+7^84.7-7^84.1

=7^84.(7^2+7-1)=7^84.55 chia het cho 55

Tick nhé

\(7^{86}+7^{85}-7^{84}=7^{84}.7^2+7^{84}.7+7^{84}.1\)

\(=7^{84}.\left(49+7-1\right)=7^{84}.55=7^{84}.5.11\)

Chia het cho 55 

Bạn bỏ bước cuối nhé !!!

a) \(16^7-2^{24}\)

\(=268435456-16777216\)

\(=251658240\)

Mà \(251658240\)chia hết cho 15

\(\Rightarrow16^7-2^{24}\)chia hết cho 15

b) \(7^{80}+7^{85}-7^{84}\)

\(=7^{84}\left(7^2+7-1\right)\)

\(=7^{84}\left(49+7-1\right)\)

\(=7^{84}\left(56-1\right)\)

\(=7^{84}.55\)

Mà 55 luôn luôn chia hết cho 55

\(\Rightarrow7^{80}+7^{85}-7^{84}\)chia hết cho 55

c) \(16^5+2^{15}\)

\(16^5=2^{20}\)

\(\Rightarrow16^5+2^{15}=2^{20}+2^{15}\)

\(=2^{15}.2^5+2^{15}\)

\(=2^{15}\left(2^5+1\right)\)

\(=2^{15}.33\)

Mà 33 luôn luôn chia hết cho 33

\(\Rightarrow16^5+2^{15}\)chia hết cho 33

c) \(16^5+2^{15}⋮33\)

\(=\left(2^4\right)^5+2^{15}\)

\(=2^{20}+2^{15}\)

\(=2^{15}.\left(1+2^5\right)\)

\(=2^{15}.33⋮33\)

16^7-2^24

=(2^4)^7-2^24

=2^28-2^24

=2^24.2^4-2^24.1

=2^24.16-2^24.1

=2^24.(16-1)

=2^24.15 chia hết cho 15

Vậy 16^7-2^24 chia hết cho 15

7⁶ + 7⁵ - 7^{4 =} 7⁴  × ( 7² + 7 - 1)= 7⁴ × 55 nên chia hết cho 55 

= 5⁵ × 192 = 5⁵ × 6×32  nên chia hét ccho  6

=7^4.(7^2+7-1)

=7^4.55\(⋮\)55(ĐPCM)

7⁶ + 7⁵ - 7⁴ = 7⁴ . ( 7² + 7¹ - 1 ) = 7⁴ . 55

Vì 55 chia hết cho 55

=> 7⁴ . 55 chia hết cho 55

Vậy: 7⁶ + 7⁵ - 7⁴ chia hết cho 55

Hk tốt