Решение:
$$(\frac{1}{2})^8 : ((\frac{1}{2})^4 : (\frac{1}{2})^6) = (\frac{1}{2})^8 : (\frac{1}{2})^{4-6} = (\frac{1}{2})^8 : (\frac{1}{2})^{-2} = (\frac{1}{2})^{8-(-2)} = (\frac{1}{2})^{10} = \frac{1}{1024}$$
Ответ: 1/1024