a: \(\dfrac{5}{2}+\dfrac{1}{2}:\left(-\dfrac{3}{4}\right)\cdot\dfrac{4}{9}-4^2-\left(-2\right)^3\)
\(=\dfrac{5}{2}+\dfrac{1}{2}\cdot\dfrac{-4}{3}\cdot\dfrac{4}{9}-16+8\)
\(=\dfrac{5}{2}-\dfrac{16}{54}-8\)
\(=-\dfrac{11}{2}-\dfrac{8}{27}=\dfrac{-297-16}{54}=\dfrac{-313}{54}\)
b: \(\left(\dfrac{3}{2}\right)^2-\left[0,5:2-\sqrt{81}\cdot\left(-\dfrac{1}{2}\right)^2\right]\)
\(=\dfrac{9}{4}-\left[\dfrac{1}{2}:2-9\cdot\dfrac{1}{4}\right]\)
\(=\dfrac{9}{4}-\dfrac{1}{4}+\dfrac{9}{4}=\dfrac{17}{4}\)
c: \(\left(-\sqrt{0,04}\right)\cdot\sqrt{0,01}+12,02\)
\(=-0,2\cdot0,1+12,02\)
\(=12,02-0,02=12\)
d: \(\left[\sqrt{169}-\sqrt{900}\right]-\left|-\dfrac{5}{4}\right|:\left(\dfrac{1}{3}-\dfrac{1}{2}\right)^2\)
\(=13-30-\dfrac{5}{4}:\left(-\dfrac{1}{6}\right)^2\)
\(=-17-\dfrac{5}{4}\cdot36=-17-45=-62\)
