$a)\frac{{\sout{3}}^1}{{\sout{5}}^1}\cdot \frac{7}{{\sout{18}}^6}\cdot \frac{{\sout{10}}^2}{21}=\frac{{\sout{7}}^1}{{\sout{6}}^3}\cdot \frac{{\sout{2}}^1}{{\sout{21}}^3}=\frac{1}{9}$  

$b)\frac{{\sout{3}}^1}{{\sout{16}}^1}\cdot \frac{{\sout{32}}^2}{35}\cdot \frac{7}{{\sout{15}}^5}=\frac{2}{{\sout{35}}^5}\cdot \frac{{\sout{7}}^1}{5}=\frac{2}{25}$  

$c)\frac{{\sout{33}}^{11}}{{\sout{8}}^4}\cdot \frac{{\sout{22}}^{11}}{{\sout{45}}^{15}}\cdot \frac{27}{121}=\frac{{\sout{11}}^1}{4}\cdot \frac{{\sout{11}}^1}{{\sout{15}}^5}\cdot \frac{{\sout{27}}^9}{{\sout{121}}^1}=\frac{9}{20}$  

$d)\frac{{\sout{25}}^5}{27}\cdot \frac{49}{{\sout{20}}^4}\cdot \frac{36}{35}=\frac{5}{{\sout{27}}^3}\cdot \frac{{\sout{49}}^7}{4}\cdot \frac{{\sout{36}}^4}{{\sout{35}}^5}=\frac{{\sout{5}}^1}{3}\cdot \frac{7}{{\sout{4}}^1}\cdot \frac{{\sout{4}}^1}{{\sout{5}}^1}=\frac{7}{3}$