3) a) (3^{2})^{-1}; б) \(\left(\frac{1}{2}\right)^{-3}\)^{-2}; в) (0,1^{-2})^{6}; г) \(\left(\frac{1}{6}\right)^{-2}\)^{0}

Решение:

1. \( (3^{2})^{-1} = 3^{2 \cdot (-1)} = 3^{-2} = \frac{1}{3^{2}} = \frac{1}{9} \)
2. \( \left(\frac{1}{2}\right)^{-3}\)^{-2} = \(\left\)\(\frac{1}{2}\right\)^{(-3) \(\cdot\) (-2)} = \(\left\)\(\frac{1}{2}\right\)^{6} = \(\frac{1^{6}}{2^{6}}\) = \(\frac{1}{64}\) \)
3. \( (0,1^{-2})^{6} = (0,1)^{(-2) \cdot 6} = (0,1)^{-12} = \left(\frac{1}{10}\right)^{-12} = 10^{12} \)
4. \( \left(\frac{1}{6}\right)^{-2}\)^{0} = \(\left\)\(\frac{1}{6}\right\)^{(-2) \(\cdot\) 0} = \(\left\)\(\frac{1}{6}\right\)^{0} = 1 \)

Ответ: 3) а) \(\frac{1}{9}\); б) \(\frac{1}{64}\); в) \(10^{12}\); г) 1.