ЗАДАНИЕ №6 Вычислите: \(\left(\frac{14}{25}-\frac{9}{25}\right)^{2}-\frac{5}{81} \cdot \left(\frac{3}{5}\right)^{3}=\)

Вычислим:

1. \(\frac{14}{25}-\frac{9}{25}=\frac{14-9}{25}=\frac{5}{25}=\frac{1}{5}\)
2. \(\left(\frac{1}{5}\right)^{2} = \frac{1^{2}}{5^{2}} = \frac{1}{25}\)
3. \(\left(\frac{3}{5}\right)^{3} = \frac{3^{3}}{5^{3}} = \frac{27}{125}\)
4. \(\frac{5}{81} \cdot \frac{27}{125} = \frac{5 \cdot 27}{81 \cdot 125} = \frac{5 \cdot 27}{27 \cdot 3 \cdot 5 \cdot 25} = \frac{1}{3 \cdot 25} = \frac{1}{75}\)
5. \(\frac{1}{25} - \frac{1}{75} = \frac{1 \cdot 3}{25 \cdot 3} - \frac{1}{75} = \frac{3}{75} - \frac{1}{75} = \frac{3-1}{75} = \frac{2}{75}\)

Ответ: \(\frac{2}{75}\)