1) $$x^6 \cdot x^7 = x^{6+7} = x^{13}$$
2) $$x^7 : x^6 = x^{7-6} = x^1 = x$$
3) $$(x^5)^8 = x^{5 \cdot 8} = x^{40}$$
4) $$\frac{(x^8)^3 \cdot x^{-2}}{x^9} = \frac{x^{8\cdot 3} \cdot x^{-2}}{x^9} = \frac{x^{24} \cdot x^{-2}}{x^9} = \frac{x^{24-2}}{x^9} = \frac{x^{22}}{x^9} = x^{22-9} = x^{13}$$
Ответ: 1) $$x^{13}$$, 2) $$x$$, 3) $$x^{40}$$, 4) $$x^{13}$$