Найдите значение степени: a) \(\left(\frac{1}{7}\right)^{3}\); б) \(\left(\frac{3}{5}\right)^{2}\); в) \(\left(\frac{1}{10}\right)^{3}\); г) \(\left(\frac{2}{5}\right)^{3}\); д) \(\left(\frac{1}{3}\right)^{3}\); e) \(\left(1\frac{1}{2}\right)^{3}\);

Ответ: a) \(\frac{1}{343}\); б) \(\frac{9}{25}\); в) \(\frac{1}{1000}\); г) \(\frac{8}{125}\); д) \(\frac{1}{27}\); e) \(\frac{27}{8}\)

Решаем:

1. a) \(\left(\frac{1}{7}\right)^{3} = \frac{1^3}{7^3} = \frac{1}{343}\)
2. б) \(\left(\frac{3}{5}\right)^{2} = \frac{3^2}{5^2} = \frac{9}{25}\)
3. в) \(\left(\frac{1}{10}\right)^{3} = \frac{1^3}{10^3} = \frac{1}{1000}\)
4. г) \(\left(\frac{2}{5}\right)^{3} = \frac{2^3}{5^3} = \frac{8}{125}\)
5. д) \(\left(\frac{1}{3}\right)^{3} = \frac{1^3}{3^3} = \frac{1}{27}\)
6. е) \(\left(1\frac{1}{2}\right)^{3} = \left(\frac{3}{2}\right)^{3} = \frac{3^3}{2^3} = \frac{27}{8}\)

Ответ: a) \(\frac{1}{343}\); б) \(\frac{9}{25}\); в) \(\frac{1}{1000}\); г) \(\frac{8}{125}\); д) \(\frac{1}{27}\); e) \(\frac{27}{8}\)