6114 3 - 3号. 흙).승.

Решение:

a) $$6 \frac{1}{4^3} - 3 \frac{3}{5} \cdot (\frac{5}{6})^2$$

1. $$6 \frac{1}{4^3} = \frac{6 \cdot 4^3 + 1}{4^3} = \frac{6 \cdot 64 + 1}{64} = \frac{384 + 1}{64} = \frac{385}{64}$$
2. $$3 \frac{3}{5} = \frac{3 \cdot 5 + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5}$$
3. $$(\frac{5}{6})^2 = \frac{5^2}{6^2} = \frac{25}{36}$$
4. $$\frac{18}{5} \cdot \frac{25}{36} = \frac{18 \cdot 25}{5 \cdot 36} = \frac{18 \cdot 5 \cdot 5}{5 \cdot 18 \cdot 2} = \frac{5}{2} = 2 \frac{1}{2}$$
5. $$\frac{385}{64} - \frac{5}{2} = \frac{385}{64} - \frac{5 \cdot 32}{2 \cdot 32} = \frac{385}{64} - \frac{160}{64} = \frac{385 - 160}{64} = \frac{225}{64} = 3 \frac{33}{64}$$

Ответ: $$3 \frac{33}{64}$$