Đáp án:

Giải thích các bước giải:

c/

`16^5 + 2^15`

`= (2^4)^5 + 2^15`

`= 2^20 + 2^15`

`= 2^15 (2^5 + 1)`

`= 2^15 * 33`

`= 11 * 3 * 2^15`

`=> 16^5 + 2^15 \vdots 11` (đfcm)

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d/

`7^6 + 7^5 - 7^4`

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

`= 7^4(49 + 7 - 1)`

`= 7^4 * 55`

`= 11 * 5 * 7^4`

`=> 7^6 + 7^5 - 7^4 \vdots 11` (đfcm)

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e/

`10^9 + 10^8 + 10^7`

`= 10^7(10^2 + 10+1)`

`= 10^7(100 + 10 + 1)`

`= 10^7 * 111`

`= 1110 * 10^6`

`= 222 * 5 * 10^6`

`=> 10^9 + 10^8 + 10^7 \vdots 222` (đfcm)

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f/

`81^7 - 27^9 - 9^13`

`= (3^4)^7 - (3^3)^9 - (3^2)^13`

`= 3^28 - 3^27 - 3^26`

`= 3^26(3^2 - 3 - 1)`

`= 3^26(9 - 3 - 1)`

`= 3^26 * 5`

`= 3^24 * 3^2 * 5`

`= 3^24 * 45`

`=> 81^7 - 27^9 - 9^13 \vdots 45` (đfcm)

`c,`

`16^5 + 2^15 = 2^20 + 2^15 = 2^15 . 2^5 + 2^15 . 1  = 2^15 . (2^5 + 1) = 2^15 . 33`

Vì `33 vdots 11`

`=> 16^5 + 2^15 vdots 11`

`d,`

`7^6+ 7^5 - 7^4 = 7^4 . 7^2 + 7^4 . 7 - 7^4 . 1 = 7^4 . (7^2 + 7 - 1) = 7^4 . 55`

Vì `55 vdots 11`

`=> 7^6+ 7^5 - 7^4 vdots 11`

`e,`

`10^9 + 10^8 + 10^7 = 10^7 . 10^2 + 10^7 . 10 + 10^7 . 1 = 10^7 . (10^2 + 10 + 1) = 10^7 . 111`

Vì `10^7 vdots 2 ; 111 vdots 111`

`=> 10^9 + 10^8 + 10^7 vdots 2.111 = 222`

`f,`

`81^7 - 27^9 - 9^13 = 3^28 - 3^27 - 3^26 = 3^26 . (3^2 - 3 - 1) = 3^24 . 3^2 . 5 = 3^24 . 45`

Vì `45 vdots 45`

`=> 81^7 - 27^9 - 9^13 vdots 45.`