Вычислите: (9/10)^6*(1 1/9)^8.

\[\left( \frac{9}{10} \right)^{6} \cdot \left( 1\frac{1}{9} \right)^{8} = \left( \frac{9}{10} \right)^{6} \cdot \left( \frac{10}{9} \right)^{8} =\]

\[= \frac{9^{6} \cdot 10^{8}}{10^{6} \cdot 9^{8}} = \frac{10^{2}}{9^{2}} = \frac{100}{81} = 1\frac{19}{81}\]