6) \(\frac{7k^{8}}{9mp} \cdot \frac{27m^{3}}{56k^{6}p^{2}}\).

6) Упростим выражение:

$$ \frac{7k^{8}}{9mp} \cdot \frac{27m^{3}}{56k^{6}p^{2}} = \frac{7 \cdot 27}{9 \cdot 56} \cdot \frac{k^{8}}{k^{6}} \cdot \frac{m^{3}}{m} \cdot \frac{1}{p \cdot p^{2}} = \frac{7 \cdot 3}{1 \cdot 56} \cdot k^{8-6} \cdot m^{3-1} \cdot \frac{1}{p^{1+2}} = \frac{21}{56} \cdot k^{2} \cdot m^{2} \cdot \frac{1}{p^{3}} = \frac{3}{8} \cdot \frac{k^{2}m^{2}}{p^{3}} = \frac{3k^{2}m^{2}}{8p^{3}} $$

Ответ: $$\frac{3k^{2}m^{2}}{8p^{3}}$$