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a: =6/35x39/54=13/105
b: \(=\dfrac{-5}{7}\left(\dfrac{2}{11}+\dfrac{9}{11}\right)+\dfrac{12}{7}=\dfrac{-5}{7}+\dfrac{12}{7}=1\)
\(\dfrac{-5}{7}.\dfrac{2}{11}-\dfrac{5}{11}.\dfrac{9}{7}-2\dfrac{5}{7}\)
\(=\dfrac{-2}{7}.\dfrac{5}{11}-\dfrac{5}{11}.\dfrac{9}{7}-\dfrac{19}{7}\)
\(=\dfrac{5}{11}.\left(\dfrac{-2}{7}-\dfrac{9}{7}\right)-\dfrac{19}{7}\)
\(=\dfrac{5}{11}.\dfrac{-11}{7}-\dfrac{19}{7}\)
\(=\dfrac{-5}{7}-\dfrac{19}{7}\)
\(=\dfrac{-24}{7}\)
\(\dfrac{-5}{7}.\dfrac{2}{11}-\dfrac{5}{11}.\dfrac{9}{7}-2\dfrac{5}{7}\)
\(=\dfrac{-2}{7}.\dfrac{5}{11}-\dfrac{5}{11}.\dfrac{9}{7}-\dfrac{19}{7}\)
\(=\dfrac{5}{7}\left(\dfrac{-2}{7}-\dfrac{9}{7}\right)-\dfrac{19}{7}\)
\(=\dfrac{5}{7}.\dfrac{-11}{7}-\dfrac{19}{7}\)
\(=\dfrac{5.\left(-11\right)}{11.7}-\dfrac{19}{7}\)
\(=\dfrac{-5.11}{11.7}-\dfrac{19}{7}\)
\(=\dfrac{-5}{7}-\dfrac{19}{7}\)
\(=\dfrac{-5-19}{7}\)
\(=\dfrac{\left(-5\right)+\left(-19\right)}{7}\)
\(=\dfrac{-24}{7}\)
\(\dfrac{-3}{7}.\dfrac{2}{11}+\left(\dfrac{-3}{7}\right).\dfrac{9}{11}+1.\left(\dfrac{-3}{7}\right)=\left(\dfrac{-3}{7}\right).\left(\dfrac{2}{11}+\dfrac{9}{11}+1\right)=\left(\dfrac{-3}{7}\right).\left(1+1\right)=\dfrac{-3}{7}.2=\dfrac{-6}{7}\)
\(\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}\times-\dfrac{7}{11}=\dfrac{-5}{11}\)
b: \(27D=3^{14}+3^{17}+...+3^{2024}\)
\(\Leftrightarrow26D=3^{2024}-3^{11}\)
hay \(D=\dfrac{3^{2024}-3^{11}}{26}\)
c: \(25E=-5^4-5^6-...-5^{1002}\)
\(\Leftrightarrow24E=-5^{1002}+5^2\)
hay \(E=\dfrac{-5^{1002}+5^2}{24}\)
\(\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{8}{11}-\dfrac{5}{7}.\dfrac{2}{11}\)
= \(\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{8}{11}-\dfrac{2}{11}\right)\)
= \(\dfrac{5}{7}.\dfrac{5+8-2}{11}\)
= \(\dfrac{5}{7}.\dfrac{11}{11}\)
= \(\dfrac{5}{7}.1=\dfrac{5}{7}\)
\(\frac{22}{25}\times\frac{5}{11}-\frac{33}{25}:\frac{11}{5}+\frac{58}{11}\)
\(=\frac{22}{25}\times\frac{5}{11}-\frac{33}{25}\times\frac{5}{11}+\frac{58}{11}\)
\(=\frac{5}{11}\times\left(\frac{22}{25}+\frac{33}{25}\right)+\frac{58}{11}\)
\(=\frac{5}{11}\times\frac{11}{5}+\frac{58}{11}\)
\(=1+\frac{58}{11}\)
\(=\frac{11}{11}+\frac{58}{11}\)
\(=\frac{69}{11}\)
\(8\frac{3}{11}-\left(3\frac{5}{7}-7\frac{8}{11}\right)\)
\(=\frac{91}{11}-\left(\frac{26}{7}-\frac{85}{11}\right)\)
\(=\frac{91}{11}-\frac{26}{7}+\frac{85}{11}\)
\(=\frac{91}{11}+\frac{85}{11}-\frac{26}{7}\)
\(=16-\frac{26}{7}\)
\(=\frac{86}{7}\)
\(\frac{5}{6}x+325\%=\frac{3}{2}x-30,75\)
\(=>\frac{5}{6}x+3,25=\frac{3}{2}x-30,75\)
\(=>\frac{5}{6}x-\frac{3}{2}x=-30,75-3,25\)
\(=>\frac{-2}{3}x=-34\)
\(=>x=-34:\left(-\frac{2}{3}\right)\)
\(=>x=-34.\left(\frac{3}{-2}\right)\)
\(=>x=51\)