a, Ta có :

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

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

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

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

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

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

\(=2^{17}.14⋮14\)

\(\Leftrightarrow8^7-2^{18}⋮14\rightarrowđpcm\)

b, \(10^6-5^7\)

\(=\left(2.5\right)^6-5^7\)

\(=2^6.5^6-5^7\)

\(=2^6.5^6-5^6.5\)

\(=5^6\left(2^6-5\right)\)

\(=5^6.59⋮59\)

\(\Leftrightarrow10^6-5^7⋮59\rightarrowđpcm\)

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

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

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

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

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

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

\(=2^{17}.14⋮14\rightarrowđpcm\)

\(10^6-5^7\)

\(=\left(2.5\right)^6-5^7\)

\(=2^6.5^6-5^7\)

\(=64.5^6-5^6.5\)

\(=5^6\left(64-5\right)\)

\(=5^6.59⋮59\rightarrowđpcm\)

a )

Ta có :

8⁷ - 2¹⁸ = ( 2³ )⁷ - 2¹⁸= 2²¹ -  2¹⁸ = 2¹⁸ ( 2³ - 1 ) = 2¹⁸ . 7 = 2¹⁷ .2.7 = 2¹⁷ . 14 ( chia hết cho 14 )

Vậy 8⁷-2¹⁸chia hết cho 14

b )

Ta có 106 - 57 = 26 . 56 - 57

= 56 . (26 - 5)

= 56 . (64 - 5)

= 56 . 59 chia hết cho 59

Vậy 106 - 57 chia hết cho 59

c ) 

sai đề à

sai thì sorry nha

tớ nghĩ tớ sai 

tớ sai thì cho cho sorry nhé

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

\(10^6-5^7=\left(2.5\right)^6-5^7=2^6.5^6-5^7=5^6.\left(2^6-5\right)=5^5.59⋮59.\)

a) Ta có : \(8^7-2^{18}=\left(2^3\right)^7-2^{17+1}\)

\(\Rightarrow8^7-2^{18}=2^{3\times7}-2^{17}\times2^1\)

\(\Rightarrow8^7-2^{18}=2^{21}-2^{17}\times2\)

\(\Rightarrow8^7-2^{18}=2^{17+4}-2^{17}\times2\)

\(\Rightarrow8^7-2^{18}=2^{17}\times2^4-2^{17}\times2\)

\(\Rightarrow8^7-2^{18}=2^{17}\left(2^4-2\right)\)

\(\Rightarrow8^7-2^{18}=2^{17}\left(16-2\right)\)

\(\Rightarrow8^7-2^{18}=2^{17}\times14\)

\(\Rightarrow\left(8^7-2^{18}\right)⋮14\left(\text{vì }14⋮14\right)\)

b) Ta có : \(10^6-5^7=\left(2\times5\right)^6-5^{6+1}\)

\(\Rightarrow10^6-5^7=2^6\times5^6-5^6\times5^1\)

\(\Rightarrow10^6-5^7=5^6\left(2^6-5^1\right)\)

\(\Rightarrow10^6-5^7=5^6\left(64-5\right)\)

\(\Rightarrow10^6-5^7=5^6\times59\)

\(\Rightarrow\left(10^6-5^7\right)⋮59\left(\text{vì }59⋮59\right)\)

Theo tớ câu b) sai cậu à

b) 10⁶ - 5⁷ chia hết cho 59

Đấy là theo tớ sai thì thôi nha

Chúc cậu hok tốt ~

a) Ta có : 8⁷ - 2¹⁸  = ( 2³)⁷ - 2^{17+ 1}

=> 8⁷ - 2¹⁸ = 2^{3 x 7} - 2¹⁷ x  2¹

=> 8⁷ - 2¹⁸ = 2²¹ - 2¹⁷ x 2

=> 8⁷ - 2¹⁸ = 2^{17 + 4} - 2¹⁷ x 2

=> 8⁷ - 2¹⁸ = 2¹⁷ x 2⁴ - 2¹⁷ x 2

=> 8⁷ - 2¹⁸ = 2¹⁷ x ( 2⁴ - 2 )

=> 8⁷ - 2¹⁸ = 2¹⁷ x ( 16 - 2 )

=> 8⁷ - 2¹⁸ = 2¹⁷ x 14

=> 8⁷ - 2¹⁸ chia hết cho 4 ( vì phân tích có thừa số 14 )

b) Ta có : 10⁶ - 5⁷ = ( 2 x 5 )⁶ - 5^{6 + 1}

=> 10⁶ - 5⁷ = 2⁶ x 5⁶ - 5⁶ x 5¹

=> 10⁶ - 5⁷ = 5⁶ x ( 2⁶ - 5¹ )

=> 10⁶ - 5⁷ = 5⁶ x ( 64 - 5 )

=> 10⁶ - 5⁷ = 5⁶ x 59

=> 10⁶ - 5⁷ chia hết cho 59 ( vì phân tích ra có thừa số 59 )

Câu a) là chia hết cho 14 nha viết nhầm 

b: \(8^{12}-2^{33}-2^{30}\)

\(=2^{36}-2^{33}-2^{30}\)

\(=2^{30}\left(2^6-2^3-1\right)=2^{30}\cdot55⋮55\)

c: \(8^7-2^{18}=2^{21}-2^{18}\)

\(=2^{18}\left(2^3-1\right)=2^{17}\cdot14⋮14\)

d: \(10^6-5^7\)

\(=2^6\cdot5^6-5^7\)

\(=5^6\left(2^6-5\right)=5^6\cdot59⋮59\)

a) 10⁶ - 5⁷

= 2⁶ . 5⁶ - 5⁷

= 5⁶ . (2⁶ - 5)

= 5⁶ . (64 - 5)

= 5⁶ . 59 chia hết cho 59

=> đpcm

b) 81⁷ - 27⁹ - 9¹³

= (3⁴)⁷ - (3³)⁹ - (3²)¹³

= 3²⁸ - 3²⁷ - 3²⁶

= 3²⁶ .(3² - 3 - 1)

= 3²⁶ . (9 - 3 - 1)

= 3²⁴ . 3² . 5

= 3²⁴ . 9 . 5

= 3²⁴ . 45 chia hết cho 45

=> đpcm

c) 8⁷ - 2¹⁸

= (2³)⁷ - 2¹⁸

= 2²¹ - 2¹⁸

= 2¹⁸ . (2³ - 1)

= 2¹⁸ (8 - 1)

= 2¹⁷ . 2 . 7

= 2¹⁷ . 14 chia hết cho 14

=> đpcm

d) 10⁹ + 10⁸ + 10⁷

= 10⁷ . (10² + 10 + 1)

= 5⁷ . 2⁷ . (100 + 10 + 1)

= 5⁷ . 2⁶ . 2 . 111

= 5⁷ . 2⁶ . 222 chia hết cho 222

=> đpcm

a: \(8^7-2^{18}=2^{21}-2^{18}=2^{18}\cdot7=2^{17}\cdot14⋮14\)

b: \(10^6-5^7=5^6\cdot2^6-5^7=5^6\cdot\left(2^6-5\right)=5^6\cdot59⋮59\)