6) б) 16⁻⁵ : 8⁻⁶; в) ((-6)⁻⁹ ⋅ 6⁻⁷) / 6⁻¹⁵;

Решение:

1. \( 16^{-5} : 8^{-6} = (2^4)^{-5} : (2^3)^{-6} = 2^{4 \cdot (-5)} : 2^{3 \cdot (-6)} = 2^{-20} : 2^{-18} = 2^{-20 - (-18)} = 2^{-20+18} = 2^{-2} = \frac{1}{2^2} = \frac{1}{4} \)
2. \( \frac{(-6)^{-9} \cdot 6^{-7}}{6^{-15}} = \frac{(-1)^{-9} \cdot 6^{-9} \cdot 6^{-7}}{6^{-15}} = \frac{-1 \cdot 6^{-9-7}}{6^{-15}} = \frac{-6^{-16}}{6^{-15}} = -6^{-16 - (-15)} = -6^{-16+15} = -6^{-1} = -\frac{1}{6} \)

Ответ: 1) \(\frac{1}{4}\); 2) \(-\frac{1}{6}\).