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a) \(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4\left(49+7-1\right)=7^4.55⋮55\)
b) \(16^5+2^{15}=\left(2^4\right)^5+2^{15}=2^{20}+2^{15}=2^{15}\left(2^5+1\right)=2^{15}\left(32+1\right)=2^{15}.33⋮33\)
c) \(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}=3^{28}-3^{27}-3^{26}=3^{26}\left(3^2-3-1\right)=3^{26}.5=3^{22}.3^4.5=3^{22}.405⋮405\)
a: \(=7^4\left(7^2+7-1\right)=7^4\cdot55⋮55\)
b: \(=2^{20}+2^{15}=2^{15}\left(2^5+1\right)=2^{15}\cdot33⋮33\)
c: \(=3^{28}-3^{27}-3^{26}=3^{26}\left(3^2-3-1\right)=3^{26}\cdot5=3^{22}\cdot405⋮405\)
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3x = 81
<=> x=4
b) x2=81
<=> x = 9;-9
c) (2x+3)3=125
<=> (2x+3)3=53
<=> 2x+3 = 5
<=> 2x=2
<=> x=1
d) (2x-3)4 = 625
<=>(2x-3)4=54
<=> 2x-3=5
<=> 2x=8
<=> x=4
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Bài 2:
a) Ta có: \(3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)
\(=3^{n+1}\cdot10+2^{n+3}\cdot3⋮6\)
b) Ta có: \(4^{13}+32^5-8^8\)
\(=2^{26}+2^{25}-2^{24}\)
\(=2^{24}\left(2^2+2-1\right)\)
\(=2^{24}\cdot5⋮5\)
c) Ta có: \(2014^{100}+2014^{99}\)
\(=2014^{99}\left(2014+1\right)\)
\(=2014^{99}\cdot2015⋮2015\)
![](https://rs.olm.vn/images/avt/0.png?1311)
11n + 2 + 122n + 1 = 121 . 11n + 12 . 144n
=(133 – 12) . 11n + 12 . 144n = 133 . 11n + (144n – 11n) . 12
Ta có: 133 . 11n chia hết 133; 144n – 11n chia hết (144 – 11)
144n – 11n chia hết 133 11n + 2 + 122n + 1 chia hết cho 133
chúc bạn học tốt !!!