2.266 Выполните действие: а) \((\frac{1}{4})^2\); б) \((\frac{3}{5})^3\); в) \((\frac{9}{11})^3\); г) \((\frac{5}{6})^3\).

a) \((\frac{1}{4})^2\) = \(\frac{1}{4}\) · \(\frac{1}{4}\) = \(\frac{1 \cdot 1}{4 \cdot 4}\) = \(\frac{1}{16}\)

Ответ: \(\frac{1}{16}\)

б) \((\frac{3}{5})^3\) = \(\frac{3}{5}\) · \(\frac{3}{5}\) · \(\frac{3}{5}\) = \(\frac{3 \cdot 3 \cdot 3}{5 \cdot 5 \cdot 5}\) = \(\frac{27}{125}\)

Ответ: \(\frac{27}{125}\)

в) \((\frac{9}{11})^3\) = \(\frac{9}{11}\) · \(\frac{9}{11}\) · \(\frac{9}{11}\) = \(\frac{9 \cdot 9 \cdot 9}{11 \cdot 11 \cdot 11}\) = \(\frac{729}{1331}\)

Ответ: \(\frac{729}{1331}\)

г) \((\frac{5}{6})^3\) = \(\frac{5}{6}\) · \(\frac{5}{6}\) · \(\frac{5}{6}\) = \(\frac{5 \cdot 5 \cdot 5}{6 \cdot 6 \cdot 6}\) = \(\frac{125}{216}\)

Ответ: \(\frac{125}{216}\)