$\frac{3a^4{b}^3}{10c^5}\ast <!--\; \ast \; -->\frac{4b^4{c}^2}{27a^7}:\frac{5b^7}{9a^3{c}^3}=\frac{3a^4{b}^3}{10c^5}\ast <!--\; \ast \; -->\frac{4b^4{c}^2}{27a^7}\ast <!--\; \ast \; -->\frac{9a^3{c}^3}{5b^7}=\frac{1}{5}\ast <!--\; \ast \; -->\frac{2}{1}\ast <!--\; \ast \; -->\frac{1}{5}=\frac{2}{25}$

$\frac{3a^2}{2b^2{c}^2}:\frac{7c^8}{6b^3}:\frac{9ab}{14c^{12}}=\frac{3a^2}{2b^2{c}^2}\ast <!--\; \ast \; -->\frac{6b^3}{7c^8}\ast <!--\; \ast \; -->\frac{14c^{12}}{9ab}=\frac{a}{1}\ast <!--\; \ast \; -->\frac{1}{1}\ast <!--\; \ast \; -->\frac{2c^2}{1}=2a{c}^2$

$(\frac{5a^3}{b^4}{)}^4\ast <!--\; \ast \; -->\frac{b^{18}}{50a^{16}}=\frac{5^4{a}^{12}}{b^{16}}\ast <!--\; \ast \; -->\frac{b^{18}}{2\ast <!--\; \ast \; -->5^2{a}^{16}}=\frac{5^2}{1}\ast <!--\; \ast \; -->\frac{b^2}{2a^4}=\frac{25b^2}{2a^4}$

$(\frac{3x^7}{y^{10}}{)}^4:(\frac{3x^6}{y^8}{)}^3=\frac{3^4{x}^{28}}{y^{40}}:\frac{3^3{x}^{18}}{y^{24}}=\frac{3^4{x}^{28}}{y^{40}}\ast <!--\; \ast \; -->\frac{y^{24}}{3^3{x}^{18}}=\frac{3x^{10}}{y^{16}}\ast <!--\; \ast \; -->\frac{1}{1}=\frac{3x^{10}}{y^{16}}$