$\frac{7}{a^2}:\frac{28}{a^8}=\frac{7}{a^2}\ast \frac{a^8}{28}=\frac{1}{1}\ast \frac{a^6}{4}=\frac{a^6}{4}$

$\frac{b^9}{8}:\frac{b^3}{48}=\frac{b^9}{8}\ast \frac{48}{b^3}=\frac{b^6}{1}\ast \frac{6}{1}=6b^6$

$\frac{27}{m^6}:\frac{36}{m^7{n}^2}=\frac{27}{m^6}\ast \frac{m^7{n}^2}{36}=\frac{3}{1}\ast \frac{m{n}^2}{4}=\frac{3m{n}^2}{4}$

$\frac{6x^{10}}{y^8}:(30x^5{y}^2)=\frac{6x^{10}}{y^8}\ast \frac{1}{30x^5{y}^2}=\frac{x^5}{y^8}\ast \frac{1}{5y^2}=\frac{x^5}{5y^{10}}$

$49m^4:\frac{21m}{n^2}=49m^4\ast \frac{n^2}{21m}=7m^3\ast \frac{n^2}{3}=\frac{7m^3{n}^2}{3}$

$\frac{16x^3{y}^8}{33z^5}:(-\frac{10x^2}{55z^6})=\frac{16x^3{y}^8}{33z^5}\ast (-\frac{55z^6}{10x^2})=\frac{8x{y}^8}{3}\ast (-\frac{5z}{5})=\frac{8x{y}^8}{3}\ast (-\frac{z}{1})=-\frac{8x{y}^{8}z}{3}$