Aritmetica

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$\small \left\{\left[\dfrac{27}{4}·\dfrac{2}{3}-\left(2-\dfrac{3}{2}\right)^4 : \left(1-\dfrac{1}{2}\right)^2-\dfrac{11}{16}\right]:\dfrac{9}{8}\right\}·\left(1+\dfrac{1}{5}\right)=$

$\small =\left\{\left[\dfrac{\cancel{27}^9}{\cancel4_2}·\dfrac{\cancel2^1}{\cancel3_1}-\left(\dfrac{4-3}{2}\right)^4 : \left(\dfrac{2-1}{2}\right)^2-\dfrac{11}{16}\right]·\dfrac{8}{9}\right\}·\left(\dfrac{5+1}{5}\right)=$

$\small =\left\{\left[\dfrac{9}{2}-\left(\dfrac{1}{2}\right)^4 : \left(\dfrac{1}{2}\right)^2-\dfrac{11}{16}\right]·\dfrac{8}{9}\right\}·\dfrac{6}{5}=$

$\small =\left\{\left[\dfrac{9}{2}-\left(\dfrac{1}{2}\right)^{4-2} -\dfrac{11}{16}\right]·\dfrac{8}{9}\right\}·\dfrac{6}{5}=$

$\small =\left\{\left[\dfrac{9}{2}-\left(\dfrac{1}{2}\right)^2 -\dfrac{11}{16}\right]·\dfrac{8}{9}\right\}·\dfrac{6}{5}=$

$\small =\left\{\left[\dfrac{9}{2}-\dfrac{1}{4} -\dfrac{11}{16}\right]·\dfrac{8}{9}\right\}·\dfrac{6}{5}=$

$\small =\left\{\left[\dfrac{72-4-11}{16}\right]·\dfrac{8}{9}\right\}·\dfrac{6}{5}=$

$\small =\left\{\dfrac{57}{16}·\dfrac{8}{9}\right\}·\dfrac{6}{5}=$

$\small =\left\{\dfrac{\cancel{57}^{19}}{\cancel{16}_2}·\dfrac{\cancel8^1}{\cancel9_3}\right\}·\dfrac{6}{5}=$

$\small =\left\{\dfrac{19}{2}·\dfrac{1}{3}\right\}·\dfrac{6}{5}=$

$\small =\dfrac{19}{6}·\dfrac{6}{5}=$

$\small =\dfrac{19}{\cancel6_1}·\dfrac{\cancel6^1}{5}=$

$\small =\dfrac{19}{1}·\dfrac{1}{5}=$

$\small =\dfrac{19}{5}$