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grosso modo il metodo principale è creare un minimo comune multiplo al divisore per ogni pezzettino di espressione...

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716)

$\small \left(\dfrac{5}{3}-\dfrac{3}{11}\right) : \left[-\dfrac{8}{3}+\dfrac{6}{7}·\left(-\dfrac{7}{6}\right)^2-\dfrac{12}{11}-\left(\dfrac{5}{8}-1+\dfrac{5}{4}\right) : \left(-2+\dfrac{1}{4}\right)\right]=$

$\small =\left(\dfrac{55-9}{33}\right) : \left[-\dfrac{8}{3}+\dfrac{\cancel6^1}{\cancel7_1}·\dfrac{\cancel{49}^7}{\cancel{36}_6}-\dfrac{12}{11}-\left(\dfrac{5-8+10}{8}\right) : \left(\dfrac{-8+1}{4}\right)\right]=$ 

$\small =\dfrac{46}{33} : \left[-\dfrac{8}{3}+\dfrac{7}{6}-\dfrac{12}{11}-\dfrac{7}{8} : -\dfrac{7}{4}\right]=$

$\small =\dfrac{46}{33} : \left[-\dfrac{8}{3}+\dfrac{7}{6}-\dfrac{12}{11}-\dfrac{\cancel7^1}{\cancel8_2} · -\dfrac{\cancel4^1}{\cancel7_1}\right]=$

$\small =\dfrac{46}{33} : \left[-\dfrac{8}{3}+\dfrac{7}{6}-\dfrac{12}{11}+\dfrac{1}{2}\right]=$

$\small =\dfrac{46}{33} : \left[\dfrac{-176+77-72+33}{66}\right]=$

$\small =\dfrac{46}{33} : -\dfrac{\cancel{138}^{23}}{\cancel{66}_{11}}=$

$\small =\dfrac{46}{33} : -\dfrac{23}{11}=$

$\small =\dfrac{\cancel{46}^2}{\cancel{33}_3} · -\dfrac{\cancel{11}^1}{\cancel{23}_1}=$

$\small =\dfrac{2}{3} · -\dfrac{1}{1}=$

$\small =-\dfrac{2}{3} $

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218)

$\small \left\{\left[\dfrac{17}{5}-\left(-\dfrac{3}{10}+\dfrac{7}{4}-\dfrac{1}{2}\right)\right ] : \left[-\dfrac{4}{5}+\dfrac{5}{19}·\left(-\dfrac{2}{5}-\dfrac{9}{10}+\dfrac{7}{20}\right)\right]+\dfrac{5}{3}\right\}^8 : \left(-\dfrac{2}{3}\right)^6= $

$\small =\left\{\left[\dfrac{17}{5}-\left(\dfrac{-6+35-10}{20}\right)\right ] : \left[-\dfrac{4}{5}+\dfrac{5}{19}·\left(\dfrac{-8-18+7}{20}\right)\right]+\dfrac{5}{3}\right\}^8 : \left(-\dfrac{2}{3}\right)^6= $

$\small =\left\{\left[\dfrac{17}{5}-\dfrac{19}{20}\right ] : \left[-\dfrac{4}{5}+\dfrac{\cancel5^1}{\cancel{19}_1}·-\dfrac{\cancel{19}^1}{\cancel{20}_4}\right]+\dfrac{5}{3}\right\}^8 : \left(-\dfrac{2}{3}\right)^6= $

$\small =\left\{\left[\dfrac{68-19}{20}\right ] : \left[-\dfrac{4}{5}-\dfrac{1}{4}\right]+\dfrac{5}{3}\right\}^8 : \left(-\dfrac{2}{3}\right)^6= $

$\small =\left\{\dfrac{49}{20} : \left[\dfrac{-16-5}{20}\right]+\dfrac{5}{3}\right\}^8 : \left(-\dfrac{2}{3}\right)^6= $

$\small =\left\{\dfrac{49}{20} : -\dfrac{21}{20}+\dfrac{5}{3}\right\}^8 : \left(-\dfrac{2}{3}\right)^6= $

$\small =\left\{\dfrac{\cancel{49}^7}{\cancel{20}_1} · -\dfrac{\cancel{20}^1}{\cancel{21}_3}+\dfrac{5}{3}\right\}^8 : \left(-\dfrac{2}{3}\right)^6= $

$\small =\left\{-\dfrac{7}{3}+\dfrac{5}{3}\right\}^8 : \left(-\dfrac{2}{3}\right)^6= $

$\small =\left\{-\dfrac{2}{3}\right\}^8 : \left(-\dfrac{2}{3}\right)^6= $

$\small = \left(-\dfrac{2}{3}\right)^{8-6}= $

$\small = \left(-\dfrac{2}{3}\right)^2= $

$\small = \dfrac{4}{9}$