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$\left\{\dfrac{7}{4}-\left[\left(\dfrac{3}{22}+\dfrac{1}{33}\right)^2·\dfrac{3^2}{5}+\dfrac{3}{2^2}\right]^2 : \left(\dfrac{4}{5}\right)^2\right\}^2 : \left(\dfrac{7}{8}-\dfrac{1}{2}\right)=$

$=\left\{\dfrac{7}{4}-\left[\left(\dfrac{9+2}{66}\right)^2·\dfrac{9}{5}+\dfrac{3}{4}\right]^2 : \dfrac{16}{25}\right\}^2 : \left(\dfrac{7-4}{8}\right)=$

$=\left\{\dfrac{7}{4}-\left[\left(\dfrac{\cancel{11}^1}{\cancel{66}_6}\right)^2·\dfrac{9}{5}+\dfrac{3}{4}\right]^2 ·\dfrac{25}{16}\right\}^2 : \dfrac{3}{8}=$

$=\left\{\dfrac{7}{4}-\left[\left(\dfrac{1}{6}\right)^2·\dfrac{9}{5}+\dfrac{3}{4}\right]^2 ·\dfrac{25}{16}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-\left[\dfrac{1}{36}·\dfrac{9}{5}+\dfrac{3}{4}\right]^2 ·\dfrac{25}{16}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-\left[\dfrac{1}{\cancel{36}_4}·\dfrac{\cancel9^1}{5}+\dfrac{3}{4}\right]^2 ·\dfrac{25}{16}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-\left[\dfrac{1}{4}·\dfrac{1}{5}+\dfrac{3}{4}\right]^2 ·\dfrac{25}{16}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-\left[\dfrac{1}{20}+\dfrac{3}{4}\right]^2 ·\dfrac{25}{16}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-\left[\dfrac{1+15}{20}\right]^2 ·\dfrac{25}{16}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-\left[\dfrac{\cancel{16}^4}{\cancel{20}_5}\right]^2 ·\dfrac{25}{16}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-\left[\dfrac{4}{5}\right]^2 ·\dfrac{25}{16}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-\dfrac{16}{25} ·\dfrac{25}{16}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-\dfrac{\cancel{16}^1}{\cancel{25}_1} ·\dfrac{\cancel{25}^1}{\cancel{16}_1}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-\dfrac{1}{1} ·\dfrac{1}{1}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7}{4}-1\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{7-4}{4}\right\}^2·\dfrac{8}{3}=$

$=\left\{\dfrac{3}{4}\right\}^2·\dfrac{8}{3}=$

$=\dfrac{9}{16}·\dfrac{8}{3}=$

$=\dfrac{\cancel9^3}{\cancel{16}_2}·\dfrac{\cancel8^1}{\cancel3_1}=$

$=\dfrac{3}{2}·\dfrac{1}{1}=$

$=\dfrac{3}{2}$