Выполнение действий:

1. $$a^5 \cdot a^4 = a^{5+4} = a^9$$
2. $$x^9 : x^3 = x^{9-3} = x^6$$
3. $$(x^4)^2 = x^{4\cdot2} = x^8$$
4. $$\frac{x^8 \cdot x^4}{x^7 \cdot x^3} = \frac{x^{8+4}}{x^{7+3}} = \frac{x^{12}}{x^{10}} = x^{12-10} = x^2$$
5. $$\frac{(x^5)^3 \cdot (x^2)^4}{(x^3)^6} = \frac{x^{5\cdot3} \cdot x^{2\cdot4}}{x^{3\cdot6}} = \frac{x^{15} \cdot x^8}{x^{18}} = \frac{x^{15+8}}{x^{18}} = \frac{x^{23}}{x^{18}} = x^{23-18} = x^5$$