$\frac{(a^3{)}^6\ast <!--\; \ast \; -->a^2}{a\ast <!--\; \ast \; -->a^{19}}=\frac{a^{18}\ast <!--\; \ast \; -->a^2}{a^{20}}=\frac{a^{20}}{a^{20}}=1$

$\frac{(ab{)}^3\ast <!--\; \ast \; -->a^4}{a{b}^2}=\frac{a^3{b}^3\ast <!--\; \ast \; -->a^4}{a{b}^2}=\frac{a^7{b}^3}{a{b}^2}=a^{6}b$

$\frac{(b^6{)}^4:b}{b^{15}\ast <!--\; \ast \; -->b^8}=\frac{b^{24}:b}{b^{23}}=\frac{b^{23}}{b^{23}}=1$

$\frac{a{b}^3}{(ab{)}^3:(a^{2}b)}=\frac{a{b}^3}{a^3{b}^3:(a^{2}b)}=\frac{a{b}^3}{a{b}^2}=b$