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$a)$ $\dfrac{75}{32}.\dfrac{-18}{25}:\dfrac{27}{-8}$

$=\left(\dfrac{75}{32}.\dfrac{-18}{25}\right):\dfrac{27}{-8}$

$=-\dfrac{27}{16}:\dfrac{27}{-8}$

$=-\dfrac{27}{16}.\dfrac{-8}{27}$

$=-\dfrac{-8}{16}$

$=\dfrac{8}{16}$

$=\dfrac{1}{2}$

$b)$ $\dfrac{46}{35}:\dfrac{23}{27}:\dfrac{15}{14}$

$=\dfrac{46}{35}.\:\dfrac{27}{23}.\dfrac{14}{15}$

$=\dfrac{46.27.14}{35.23.15}$ $=\dfrac{23.2.27.14}{35.23.15}$

$=\dfrac{2.3.9.\:14}{35.15}$ $=\dfrac{2.3.9.14}{35.3.5}$

$=\dfrac{2.9.7.2}{35.5}$ $=\dfrac{2.9.7.2}{7.5.5}$

$=\dfrac{2.9.2}{5.5}$

$=\dfrac{36}{25}$