$a)\frac{5}{{\sout{6}}^1}\cdot {\sout{12}}^2=\frac{5}{1}\cdot 2=10$

$b)\frac{7}{{\sout{8}}^1}\cdot {\sout{24}}^3=\frac{7}{1}\cdot 3=21$ $b)\frac{7}{{\sout{8}}^1}\cdot {\sout{24}}^3=\frac{7}{1}\cdot 3=21$

$c)\frac{9}{{\sout{14}}^2}\cdot {\sout{7}}^1=\frac{9}{2}\cdot 1=4\frac{1}{2}$

$d)\frac{4}{{\sout{9}}^1}\cdot {\sout{36}}^4=\frac{4}{1}\cdot 4=16$

$e)\frac{7}{{\sout{15}}^5}\cdot {\sout{6}}^2=\frac{7}{5}\cdot 2=\frac{14}{5}=2\frac{4}{5}$

$f)\frac{11}{{\sout{18}}^3}\cdot {\sout{12}}^2=\frac{11}{3}\cdot 2=\frac{22}{3}=7\frac{1}{3}$