$\frac{6a^4b^2}{35c^3} * \frac{14b^2}{a^7c^5} * \frac{5a^3c^8}{18b^4} = \frac{1}{1} * \frac{2}{1} * \frac{1}{3} = \frac{2}{3}$

$\frac{33m^8}{34n^8} : \frac{88m^4}{51n^4} : \frac{21m^6}{16n^2} = \frac{33m^8}{34n^8} * \frac{51n^4}{88m^4} * \frac{16n^2}{21m^6} = \frac{1}{n^2} * \frac{3}{1} * \frac{1}{7m^2} = \frac{3}{7m^2n^2}$

$\frac{36x^6}{49y^5} : \frac{24x^9}{25y^4} * \frac{7x^2}{30y} = \frac{36x^6}{49y^5} * \frac{25y^4}{24x^9} * \frac{7x^2}{30y} = \frac{1}{7y} * \frac{5}{2x} * \frac{1}{2y} = \frac{5}{28xy^2}$

$(\frac{m^5n}{3p^3})^3 : \frac{m^{10}n^5}{54p^8} = (\frac{m^5n}{3p^3})^3 * \frac{54p^8}{m^{10}n^5} = \frac{m^{15}n^3}{27p^9} * \frac{54p^8}{m^{10}n^5} = \frac{m^{5}}{p} * \frac{2}{n^2} = \frac{2m^{5}}{n^2p}$

$(\frac{2a^5}{y^6})^4 : (\frac{4a^6}{y^8})^3 = \frac{16a^{20}}{y^{24}} : \frac{64a^{18}}{y^{24}} = \frac{16a^{20}}{y^{24}} * \frac{y^{24}}{64a^{18}} = \frac{a^{2}}{1} * \frac{1}{4} = \frac{a^{2}}{4}$

$(-\frac{27x^3}{16y^5})^2 * (\frac{8y^3}{9x^2})^3 = \frac{(3^3)^2x^6}{(2^4)^2y^{10}} * \frac{(2^3)^3y^9}{(3^2)^3x^6} = \frac{3^6x^6}{2^8y^{10}} * \frac{2^9y^9}{3^6x^6} = \frac{1}{y} * \frac{2}{1} = \frac{2}{y}$