$\frac{270a^{10}{b}^8{c}^7}{810a^4{b}^{12}c}=\frac{270}{810}\ast <!--\; \ast \; -->\frac{a^{10}}{a^4}\ast <!--\; \ast \; -->\frac{b^8}{b^{12}}\ast <!--\; \ast \; -->\frac{c^7}{c}=\frac{1}{3}\ast <!--\; \ast \; -->\frac{a^6}{1}\ast <!--\; \ast \; -->\frac{1}{b^4}\ast <!--\; \ast \; -->\frac{c^6}{1}=\frac{a^6{c}^6}{3b^4}$

$\frac{132x^5{y}^{10}{z}^{11}}{144x^6{y}^5{z}^{22}}=\frac{132}{144}\ast <!--\; \ast \; -->\frac{x^5}{x^6}\ast <!--\; \ast \; -->\frac{y^{10}}{y^5}\ast <!--\; \ast \; -->\frac{z^{11}}{z^{22}}=\frac{11}{12}\ast <!--\; \ast \; -->\frac{1}{x}\ast <!--\; \ast \; -->\frac{y^5}{1}\ast <!--\; \ast \; -->\frac{1}{z^{11}}=\frac{11y^5}{12x{z}^{11}}$

$\frac{140m^{25}{n}^{101}{r}^{64}}{42m^{14}{n}^{202}{r}^{61}}=\frac{140}{42}\ast <!--\; \ast \; -->\frac{m^{25}}{m^{14}}\ast <!--\; \ast \; -->\frac{n^{101}}{n^{202}}\ast <!--\; \ast \; -->\frac{r^{64}}{r^{61}}=\frac{10}{3}\ast <!--\; \ast \; -->\frac{m^{11}}{1}\ast <!--\; \ast \; -->\frac{1}{n^{101}}\ast <!--\; \ast \; -->\frac{r^3}{1}=\frac{10m^{11}{r}^3}{3n^{101}}$

$\frac{540p^{12}{q}^{43}{t}^{54}}{36p^2{q}^{54}{t}^{55}}=\frac{540}{36}\ast <!--\; \ast \; -->\frac{p^{12}}{p^2}\ast <!--\; \ast \; -->\frac{q^{43}}{q^{54}}\ast <!--\; \ast \; -->\frac{t^{54}}{t^{55}}=\frac{15}{1}\ast <!--\; \ast \; -->\frac{p^{10}}{1}\ast <!--\; \ast \; -->\frac{1}{q^{11}}\ast <!--\; \ast \; -->\frac{1}{t}=\frac{15p^{10}}{q^{11}t}$