$a)\frac{32}{33}=\frac{{\sout{32}}^4}{33}\cdot \frac{1}{{\sout{8}}^1}=\frac{4}{33}$

$b)\frac{51}{64}:17=\frac{{\sout{51}}^3}{64}\cdot \frac{1}{{\sout{17}}^1}=\frac{3}{64}$

$c)2\frac{1}{4}:1\frac{11}{16}=\frac{9}{4}:\frac{27}{16}=\frac{{\sout{9}}^1}{4}\cdot \frac{16}{{\sout{27}}^3}=\frac{1}{{\sout{4}}^1}\cdot \frac{{\sout{16}}^4}{3}=\frac{4}{3}=1\frac{1}{3}$

$d)10\frac{2}{3}:\frac{7}{9}=\frac{32}{3}:\frac{7}{9}=\frac{32}{{\sout{3}}^1}\cdot \frac{{\sout{9}}^3}{7}=\frac{96}{7}=13\frac{5}{7}$