2 Выполните действия: а) $$\frac{2}{5} \cdot \left(\frac{11}{14} - \frac{3}{7}\right)$$; б) $$\left(\frac{1}{3}\right)^2 + \left(\frac{1}{3}\right)^3$$.

Решение:

a) $$\frac{2}{5} \cdot \left(\frac{11}{14} - \frac{3}{7}\right)$$

1. $$\frac{11}{14} - \frac{3}{7} = \frac{11}{14} - \frac{3 \cdot 2}{7 \cdot 2} = \frac{11}{14} - \frac{6}{14} = \frac{11-6}{14} = \frac{5}{14}$$
2. $$\frac{2}{5} \cdot \frac{5}{14} = \frac{2 \cdot 5}{5 \cdot 14} = \frac{10}{70} = \frac{1}{7}$$

Ответ: $$\frac{1}{7}$$

б) $$\left(\frac{1}{3}\right)^2 + \left(\frac{1}{3}\right)^3$$

1. $$\left(\frac{1}{3}\right)^2 = \frac{1}{3} \cdot \frac{1}{3} = \frac{1}{9}$$
2. $$\left(\frac{1}{3}\right)^3 = \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} = \frac{1}{27}$$
3. $$\frac{1}{9} + \frac{1}{27} = \frac{1 \cdot 3}{9 \cdot 3} + \frac{1}{27} = \frac{3}{27} + \frac{1}{27} = \frac{3+1}{27} = \frac{4}{27}$$

Ответ: $$\frac{4}{27}$$