a, \(10^9+10^8+10^7⋮222\)
Ta có:\(10^9+10^8+10^7=10^7.\left(10^2+10+1\right)\)
\(=10^7.111=5^7.2^7.111=5^7.2^6.2.111=5^7.2^6.222\)
Vì 222\(⋮222\Rightarrow5^7.2^6.222⋮222\)
Vậy \(10^9+10^8+10^7⋮222\)
b) 817 - 279 - 913 ⋮ 45
\(\)Ta có: \(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)
\(=3^{28}-3^{27}-3^{26}=3^{26}.\left(3^2-3-1\right)\)
\(=3^{26}.5=3^{24}.3^2.5=3^{24}.45\)
Vì \(45⋮45\Rightarrow3^{24}.45⋮45\)
Vậy \(81^7-27^9-9^{13}⋮45\)
CHÚC BẠN HỌC TỐT!!
a) \(10^9+10^8+10^7\)
\(=10^7\left(10^2+10+1\right)\)
\(=5^7.2^7.\left(100+10+1\right)\)
\(=5^7.2^6.2\left(100+10+1\right)\)
\(=5^7.2^6.2.111\)
\(=5^7.2^6.222⋮222\)
a, \(10^9+10^8+10^7=10^6.\left(10^3+10^2+10\right)\)
\(=10^6.1110\)
Vì 1110 chia hết cho 222 nên \(10^6.1110\) chia hết cho 222
Vậy.................(đpcm)
b, \(81^7-27^9-9^{13}=3^{28}-3^{27}-3^{26}\)
\(=3^{24}\left(3^4-3^3-3^2\right)=3^{24}.45\)
Vì 45 chia hết cho 45 nên \(3^{24}.45\) chia hết cho 45
Vậy....................(đpcm)
Chúc bạn học tốt!!!
