Вычисление степеней

1. a) 8^-2 × 4³ = (2³)^-2 × (2²)³ = 2^-6 × 2⁶ = 2^-6+6 = 2⁰ = 1
2. б) 9^-6 × 27⁵ = (3²)^-6 × (3³)⁵ = 3^-12 × 3¹⁵ = 3^-12+15 = 3³ = 27
3. в) 10⁰ ÷ 10^-3 = 10^0-(-3) = 10³ = 1000
4. г) 125 ÷ 25^-5 = 5³ ÷ (5²)^-5 = 5³ ÷ 5^-10 = 5^3-(-10) = 5¹³ = 1220703125
5. д) $$\frac{4^{-2} \cdot 8^{-6}}{2^{-22}} = \frac{(2^2)^{-2} \cdot (2^3)^{-6}}{2^{-22}} = \frac{2^{-4} \cdot 2^{-18}}{2^{-22}} = \frac{2^{-22}}{2^{-22}} = 1$$
6. е) $$\frac{5^{-5} \cdot 25^{10}}{125^5} = \frac{5^{-5} \cdot (5^2)^{10}}{(5^3)^5} = \frac{5^{-5} \cdot 5^{20}}{5^{15}} = \frac{5^{15}}{5^{15}} = 1$$