Exercice

On a \( X=\left(\dfrac{\dfrac{\left(-\dfrac{21}{10}+3+\dfrac{131}{3}\right)-10\times\left(-3\right)\times\dfrac{91}{3}+\dfrac{21}{10}}{\dfrac{-11}{8}-\left(-\dfrac{105}{4}-\dfrac{27}{2}-\dfrac{21}{10}-\dfrac{21}{10}\right)-11}}{0}-\left(\left(-\dfrac{131}{3}+\dfrac{0}{-\dfrac{105}{4}}\right)-\dfrac{\dfrac{\left(-7\right)\times\left(-\dfrac{27}{2}\right)\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}=\dfrac{3514283475299520}{2625}\) . Voici le détail : \begin{eqnarray*} X &=&\left(\dfrac{\dfrac{\left(\dfrac{9}{10}+\dfrac{131}{3}\right)-10\times\left(-3\right)\times\dfrac{91}{3}+\dfrac{21}{10}}{\dfrac{-11}{8}-\left(-\dfrac{105}{4}-\dfrac{27}{2}-\dfrac{21}{10}-\dfrac{21}{10}\right)-11}}{0}-\left(\left(-\dfrac{131}{3}+\dfrac{0}{-\dfrac{105}{4}}\right)-\dfrac{\dfrac{\left(-7\right)\times\left(-\dfrac{27}{2}\right)\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}-10\times\left(-3\right)\times\dfrac{91}{3}+\dfrac{21}{10}}{\dfrac{-11}{8}-\left(-\dfrac{105}{4}-\dfrac{27}{2}-\dfrac{21}{10}-\dfrac{21}{10}\right)-11}}{0}-\left(\left(-\dfrac{131}{3}+\dfrac{0}{-\dfrac{105}{4}}\right)-\dfrac{\dfrac{\left(-7\right)\times\left(-\dfrac{27}{2}\right)\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}-\left(-30\right)\times\dfrac{91}{3}+\dfrac{21}{10}}{\dfrac{-11}{8}-\left(-\dfrac{105}{4}-\dfrac{27}{2}-\dfrac{21}{10}-\dfrac{21}{10}\right)-11}}{0}-\left(\left(-\dfrac{131}{3}+\dfrac{0}{-\dfrac{105}{4}}\right)-\dfrac{\dfrac{\left(-7\right)\times\left(-\dfrac{27}{2}\right)\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{\dfrac{-11}{8}-\left(-\dfrac{105}{4}-\dfrac{27}{2}-\dfrac{21}{10}-\dfrac{21}{10}\right)-11}}{0}-\left(\left(-\dfrac{131}{3}+\dfrac{0}{-\dfrac{105}{4}}\right)-\dfrac{\dfrac{\left(-7\right)\times\left(-\dfrac{27}{2}\right)\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}-\left(-\dfrac{105}{4}-\dfrac{27}{2}-\dfrac{21}{10}-\dfrac{21}{10}\right)-11}}{0}-\left(\left(-\dfrac{131}{3}+\dfrac{0}{-\dfrac{105}{4}}\right)-\dfrac{\dfrac{\left(-7\right)\times\left(-\dfrac{27}{2}\right)\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}-\left(-\dfrac{159}{4}-\dfrac{21}{10}-\dfrac{21}{10}\right)-11}}{0}-\left(\left(-\dfrac{131}{3}+\dfrac{0}{-\dfrac{105}{4}}\right)-\dfrac{\dfrac{\left(-7\right)\times\left(-\dfrac{27}{2}\right)\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}-\left(-\dfrac{837}{20}-\dfrac{21}{10}\right)-11}}{0}-\left(\left(-\dfrac{131}{3}+\dfrac{0}{-\dfrac{105}{4}}\right)-\dfrac{\dfrac{\left(-7\right)\times\left(-\dfrac{27}{2}\right)\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+\dfrac{0}{-\dfrac{105}{4}}\right)-\dfrac{\dfrac{\left(-7\right)\times\left(-\dfrac{27}{2}\right)\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{\left(-7\right)\times\left(-\dfrac{27}{2}\right)\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{\dfrac{189}{2}\times0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{10\times\dfrac{91}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{910}{3}\times\left(-11\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\left(-\dfrac{10010}{3}\right)\times\left(-\dfrac{131}{3}\right)}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11-0+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times\left(-11+5\right)\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{105}{4}-3-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times\left(-\dfrac{117}{4}-11\right)+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10-\left(-\dfrac{27}{2}+\dfrac{21}{10}\right)}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-7\right)\times10\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times\left(-\dfrac{11}{3}+\dfrac{11}{3}+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times\left(0+5\right)}\\&=&\left(\dfrac{\dfrac{\dfrac{1337}{30}+910+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{28637}{30}+\dfrac{21}{10}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{-\dfrac{11}{8}+\dfrac{879}{20}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1703}{40}-11}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(\left(-\dfrac{131}{3}+0\right)-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-\dfrac{\dfrac{0}{-\dfrac{11}{3}}}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-\dfrac{0}{-\dfrac{27}{2}}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{\dfrac{1311310}{9}}{10}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-10\times-6\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+60\times\left(-\dfrac{131}{3}\right)\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0-2620\times-\dfrac{161}{4}+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{-\dfrac{131}{3}+\dfrac{131}{3}-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{0-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{-10+\dfrac{57}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{\left(-70\right)\times5}\\&=&\left(\dfrac{\dfrac{\dfrac{2870}{3}}{\dfrac{1263}{40}}}{0}-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(\dfrac{\dfrac{114800}{3789}}{0}-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(0-\left(-\dfrac{131}{3}-0+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(0-\left(-\dfrac{131}{3}+7\right)+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(0+\dfrac{110}{3}+\dfrac{27}{2}-\left(-5\right)\times\left(-\dfrac{11}{3}\right)\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(0+\dfrac{110}{3}+\dfrac{27}{2}-\dfrac{55}{3}\times\left(-\dfrac{27}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(0+\dfrac{110}{3}+\dfrac{27}{2}-\left(-\dfrac{495}{2}\right)\times\dfrac{131131}{9}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(0+\dfrac{110}{3}+\dfrac{27}{2}+\dfrac{7212205}{2}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10-0+105455+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(0+\dfrac{110}{3}+\dfrac{27}{2}+\dfrac{7212205}{2}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(10+105455+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(0+\dfrac{110}{3}+\dfrac{27}{2}+\dfrac{7212205}{2}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times\left(105465+3\right)\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(0+\dfrac{110}{3}+\dfrac{27}{2}+\dfrac{7212205}{2}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times105468\times\dfrac{\dfrac{\dfrac{7}{5}}{-7}}{-350}\\&=&\left(0+\dfrac{110}{3}+\dfrac{27}{2}+\dfrac{7212205}{2}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times105468\times\dfrac{-\dfrac{1}{5}}{-350}\\&=&\left(0+\dfrac{110}{3}+\dfrac{27}{2}+\dfrac{7212205}{2}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times105468\times\dfrac{1}{1750}\\&=&\left(\dfrac{110}{3}+\dfrac{27}{2}+\dfrac{7212205}{2}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times105468\times\dfrac{1}{1750}\\&=&\left(\dfrac{301}{6}+\dfrac{7212205}{2}\right)\times10\times\left(-7\right)\times\left(-11\right)\times8\times105468\times\dfrac{1}{1750}\\&=&\dfrac{10818458}{3}\times10\times\left(-7\right)\times\left(-11\right)\times8\times105468\times\dfrac{1}{1750}\\&=&\dfrac{10818458}{3}\times10\times\left(-7\right)\times\left(-88\right)\times105468\times\dfrac{1}{1750}\\&=&\dfrac{10818458}{3}\times10\times\left(-7\right)\times\left(-9281184\right)\times\dfrac{1}{1750}\\&=&\dfrac{10818458}{3}\times10\times\left(-7\right)\times\left(-\dfrac{4640592}{875}\right)\\&=&\dfrac{108184580}{3}\times\left(-7\right)\times\left(-\dfrac{4640592}{875}\right)\\&=&\left(-\dfrac{757292060}{3}\right)\times\left(-\dfrac{4640592}{875}\right)\\&=&\dfrac{3514283475299520}{2625}\\ \end{eqnarray*}