a) ta có : \(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4.\left(49+7-1\right)=7^4.55⋮55\)

\(\Rightarrow7^4.55\) chia hết cho \(55\) \(\Leftrightarrow7^6+7^5-7^4\) chia hết cho \(55\)

vậy \(7^6+7^5-7^4\) chia hết cho \(55\) (đpcm)

b) ta có \(16^5+2^{15}=\left(2^4\right)^5+2^{15}=2^{20}+2^{15}=2^{15}\left(2^5+1\right)=2^{15}.\left(32+1\right)=2^{15}.33⋮33\)

\(\Rightarrow2^{15}.33\) chia hết cho \(33\) \(\Leftrightarrow16^5+2^{15}\) chia hết cho \(33\)

vậy \(16^5+2^{15}\) chia hết cho \(33\) (đpcm)

c) ta có \(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}=3^{28}-3^{27}-3^{26}\)

\(=3^{22}\left(3^6-3^5-3^4\right)=3^{22}\left(729-243-81\right)=3^{22}.405⋮405\)

\(\Rightarrow3^{22}.405\) chia hết cho \(405\) \(\Leftrightarrow81^7-27^9-9^{13}\) chia hết cho \(405\)

vậy \(81^7-27^9-9^{13}\) chia hết cho \(405\) (đpcm)

\(a.\)

\(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4.55⋮55\)

\(b.\)

\(16^5+2^{15}=2^{20}+2^{15}=2^{15}\left(2^5+1\right)=2^{15}.33⋮33\)

\(c.\)

Ta có : \(405=3^4.5\)

\(\Rightarrow81^7-27^9-9^{13}=3^{28}-3^{27}-3^{26}=3^{26}\left(3^2-3-1\right)=3^{26}.5⋮405\)

a ) 7⁶ + 7⁵ - 7⁴

= 7⁴ ( 7² + 7 - 1 )
= 7⁴. 55 chia hết cho 55

b ) 16⁵ + 2¹⁵

= ( 2⁴ ) ⁵ + 2¹⁵

= 2²⁰ + 2¹⁵

= 2¹⁵ ( 2⁵ + 1 )

= 2¹⁵ . 33 chia hết cho 33

c ) 81⁷ - 27⁹ - 9¹³

= ( 3⁴ )⁷ - ( 3³ )⁹ - ( 3² )¹³

= 3²⁸ - 3²⁷ - 3²⁶

= 3²⁶ ( 3² - 3 - 1 )

= 3²⁶ . 5

= 3²² . 3⁴ . 5

= 3²² . 81 . 5

= 3²² . 405 chia hết cho 405

81⁷- 27⁹-9¹³

= (3⁴)⁷-(3³)⁹-(3²)¹³

= 3²⁸-3²⁷-3²⁶

=3²⁶(3²-3-1)

=3³⁶. 5 chia hết cho 5

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)-(3^26.3^1)-(3^26.1)
=3^26.(9-3-1)
=3^22.(3^4.5)
=3^22.405 chia het cho 405
=> 81^7-27^9-9^13 chia het cho 405

Mà 405 lại chia hết cho 15 nên  81^7-27^9-9^13 chia hết cho 15

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\(=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)

\(=3^{28}-3^{27}-3^{26}\)

\(=3^{26}\left(9-3-1\right)=3^{26}.5\)chia hết cho 5

\(81^7-27^9-9^{13}\)

\(=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)

\(=3^{28}-3^{27}-3^{26}\)

\(=3^{26}\left(3^2-3-1\right)\)

\(=3^{26}\cdot5⋮5\left(đpcm\right)\)

\(81^7-27^9-9^13 =(3^4)^7-(3^3)^9-(3^2)^13 =3^28-3^27-3^26 =3^26.9-3^26.3-3^26.1 =3^26.(9-3-1) =3^26.5 ĐPCMMMMMMMMMMMMMMMMMMMM \)

a)

\(3^{21}-3^{18}\\ =3^{17}.\left(3^4-3\right)\\ =3^{17}.\left(81-3\right)\\ =3^{17}.78\)

Vì \(3^{17}.78⋮78\) nên \(3^{21}-3^{18}⋮78\) (đpcm)

Vậy...

b)
\(81^7-27^9-9^{13}\\ =\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\\ =3^{28}-3^{27}-3^{26}\\ =3^{24}.\left(3^4-3^3-3^2\right)\\ =3^{24}.\left(81-27-9\right)\\ =3^{24}.45\)

Vì \(3^{24}.45⋮45\) nên \(81^7-27^9-9^{13}⋮45\) (đpcm)

Vậy...

b) 81⁷ - 27⁹ -9¹³ chia hết cho 405

Ta có: 81⁷ - 27⁹ -9¹³ = 3²⁸- 3²⁷-3²⁶

⁼ 3²⁶(3²-3-1)

= 3²⁶. 5 = 3²². 405 chia hết cho 405 (đpcm)

a)

\(7^6+7^5-7^4=7^4.\left(7^2+7-1\right)=7^4.55\) chia hết cho 55

=>\(7^6+7^5-7^4\) chia hết cho 55

c)

\(16^5+2^{15}=2^{4.5}+2^{15}=2^{20}+2^{15}=2^{15}.\left(2^5+1\right)=2^{15}.33\)chia hết cho 33

Do đó: \(16^5+2^{15}\) chia hết cho 33