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\(\dfrac{-21}{27};\dfrac{35}{-45};\dfrac{-28}{36}\)
\(\frac{3}{14}:\frac{1}{28}-\frac{13}{21}:\frac{1}{28}+\frac{29}{42}:\frac{1}{28}-8\)
\(=\left(\frac{3}{14}-\frac{13}{21}+\frac{29}{42}\right):\frac{1}{28}-8\)
\(=\left(\frac{9}{42}-\frac{26}{21}+\frac{29}{42}\right):\frac{1}{28}-8\)
\(=\left(\frac{-17}{42}+\frac{29}{42}\right):\frac{1}{28}-8\)
\(=\frac{12}{42}:\frac{1}{28}-8\)
\(=\frac{2}{7}.28-8\)
\(=\frac{56}{7}-8\)
\(=8-8\)
\(=0\)
\(A=\left(1-\frac{1}{21}\right).\left(1-\frac{1}{28}\right).\left(1-\frac{1}{36}\right)...\left(1-\frac{1}{1326}\right)\)
\(A=\frac{20}{21}.\frac{27}{28}.\frac{35}{36}...\frac{1325}{1326}\)
\(A=\frac{40}{42}.\frac{54}{56}.\frac{70}{72}...\frac{2650}{2652}\)
\(A=\frac{5.8}{6.7}.\frac{6.9}{7.8}.\frac{7.10}{8.9}...\frac{50.53}{51.52}\)
\(A=\frac{5.6.7...50}{6.7.8...51}.\frac{8.9.10...53}{7.8.9...52}\)
\(A=\frac{5}{51}.\frac{53}{7}\)
\(A=\frac{265}{357}\)
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...
dòng cuối không biết.
28-13=15
36-15=21
39-21=18
45-18=27
99-27=72