You use a combination of the rules you have learned and get

$$\begin{array}{llll}\hfill \frac{a^4\cdot {(a^2\cdot b)}^5}{{(a\cdot b)}^3}& =\frac{a^4\cdot {(a^2)}^5\cdot b^5}{a^3\cdot b^3}& \hfill & \\ \hfill & =\frac{a^4\cdot a^{10}\cdot b^5}{a^3\cdot b^3}& \hfill & \\ \hfill & =\frac{a^{14}\cdot b^5}{a^3\cdot b^3}& \hfill & \\ \hfill & =a^{14-3}\cdot b^{5-3}& \hfill & \\ \hfill & =a^{11}{b}^2& \hfill & \end{array}$$