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a) 8110 - 2713 - 921 ⋮ 225
= ( 34)10 - ( 33 )13 - ( 32 )21
= 340 - 339 - 342
= 339(3-1-33)
= 337x9x(-25)
= 337x(-225) ⋮ 225
b) 12566 - 5197 + 2598 ⋮ 105
= (53)66-5197+(52)98
=5198-5197+5196
=5196(52-5+1)
=5196x21
=5195x5x21
=5195x105 ⋮ 105
a) 8110 - 2713 - 921 \(⋮\)225
= 8110 - 273 - 921 : 225
= ( 34 )10 - ( 33 )3 - ( 32 )21
= 340 - 39 - 342
= 339 . ( -25 )
= -225 . 337
-225 nhân 1 số tự nhiên thì luôn luôn chia hết cho 225
\(81^{10}-27^{13}-9^{21}\)
\(=\left(3^4\right)^{10}-\left(3^3\right)^{13}-\left(3^2\right)^{21}\)
\(=3^{40}-3^{39}-3^{42}\)
\(=3^{39}\left(3-1-3^3\right)\)
\(=3^{39}.\left(-25\right)\)
\(=3^{37}.3^2.\left(-25\right)\)
\(=3^{37}.\left(-225\right)⋮225\)
\(\Leftrightarrow81^{10}-27^{13}-9^{21}⋮225\left(đpcm\right)\)
a,\(\left(\frac{1}{9}-1\right).\left(\frac{1}{10}-1\right)...\left(\frac{1}{2004}-1\right).\left(\frac{1}{2005}-1\right)\)
\(=\frac{-8}{9}.\frac{-9}{10}...\frac{-2003}{2004}.\frac{-2004}{2005}\)
\(=\frac{\left(-8\right).\left(-9\right)...\left(-2003\right).\left(-2004\right)}{9.10...2004.2005}\)
\(=\frac{-\left(8.9...2003.2004\right)}{9.10...2004.2005}\)
\(=\frac{-8}{2005}\)
b,Ta có: \(81^{10}-27^{13}-9^{21}\)
\(=\left(3^4\right)^{10}-\left(3^3\right)^{13}-\left(3^2\right)^{21}\)
\(=3^{40}-3^{39}-3^{42}\)
\(=3^{39}.3-3^{39}-3^{39}.3^3\)
\(=3^{39}.\left(3-1-3^3\right)\)
\(=3^2.3^{37}.\left(-25\right)\)
\(=3^{37}.\left(-225\right)⋮225\)
Vậy \(81^{10}-27^{13}-9^{21}⋮225\)
Đúng ạk
Năm nay đứa nào cũng thấp điểm hết ròi =.= hazz
Cái chỗ : \(3^{37}\left(9.-25\right)\) phải là \(3^{37}.9.\left(-25\right)=3^{37}.\left(-225\right)\) nhé
=.=
2, 100^2+200^2+300^2+..+1000^2
=100^2+2^2×100^2+3^2×100^2+...+100^2×10^2
=100^2×( 1^2+2^2+3^2+..+10^2)
=100^2×385
= 3850000
\(A=\frac{81^4.3^{10}.27^5:3^{12}}{3^{18}:9^3.243^2}=\frac{3^{16}.3^{10}.3^{15}:3^{12}}{3^{18}:3^6.3^{10}}=\frac{3^{29}}{3^{22}}=3^7\)
\(B=\frac{2.55^2-9.55^{21}}{25^{10}}:\frac{5\left(3.7^{15}-19.7^{14}\right)}{7^{16}+3.7^{15}}=\frac{2.55^2-9.55^2.55^{19}}{25^{10}}:\frac{5\left(21.7^{14}-19.7^{14}\right)}{7.7^{15}+3.7^{15}}=\frac{55^2\left(55^{19}.9-2\right)}{25^{10}}:\frac{5.7^{14}.2}{7^{15}.10}=\frac{55^2\left(55^{19}.9-2\right)}{25^{10}}.\frac{7^{15}.10}{5.7^{14}.2}\)Chịu ==