$a\text{)}-{\left(-0,1\right)}^3-{\left(-1,3\right)}^2=-\left(-0,001\right)-1,69=0,001-1,69=-1,689$     

$b\text{)}-5\frac{5}{6}:\left(-3\frac{1}{3}\right)+\left(-5\frac{3}{4}\right):2\frac{7}{8}=-\frac{35}{6}:\left(-\frac{10}{3}\right)-\frac{23}{4}:\frac{23}{8}=-\frac{35}{6}\cdot \left(-\frac{3}{10}\right)-\frac{23}{4}\cdot \frac{8}{23}=-\frac{35}{2}\cdot \left(-\frac{1}{10}\right)-2=\frac{35}{20}-2=1\frac{3}{4}-2=-\frac{1}{4}$  

$c\text{)}{\left(5\frac{2}{3}-7\frac{1}{2}\right)}^2:3\frac{2}{3}={\left(\frac{17}{3}-\frac{15}{2}\right)}^2:\frac{11}{3}={\left(\frac{34}{6}-\frac{45}{6}\right)}^2\cdot \frac{3}{11}={\left(-\frac{11}{6}\right)}^2\cdot \frac{3}{11}=\frac{121}{36}\cdot \frac{3}{11}=\frac{11}{12}$  

$d\text{)}\sqrt[3]{3,6-\left(-4,4\right)}+\sqrt{3,6-\left(-4,4\right)}=\sqrt[3]{3,6+4,4}+\sqrt{3,6+4,4}=\sqrt[3]{8}+\sqrt{8}=2+2\sqrt{2}$