Вычислить: 81^{0.4} \cdot 3^{0.3} I 9^{0.3} \cdot 27^{6}

$$\frac{81^{0.4} \cdot 3^{0.3}}{9^{0.3} \cdot 27^{0.6}} = \frac{(3^4)^{0.4} \cdot 3^{0.3}}{(3^2)^{0.3} \cdot (3^3)^{0.6}} = \frac{3^{4 \cdot 0.4} \cdot 3^{0.3}}{3^{2 \cdot 0.3} \cdot 3^{3 \cdot 0.6}} = \frac{3^{1.6} \cdot 3^{0.3}}{3^{0.6} \cdot 3^{1.8}} = \frac{3^{1.6+0.3}}{3^{0.6+1.8}} = \frac{3^{1.9}}{3^{2.4}} = 3^{1.9 - 2.4} = 3^{-0.5} = \frac{1}{3^{0.5}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$$

Ответ: $$\frac{\sqrt{3}}{3}$$