9. Вычислите: a) 9 * 3⁴= б) 100 * (-1/5)^(-2) = в) 3^(-1) + 2^(-3) = г) 0,2⁰ – 0,1^(-3) = д) 36 * (-3)^(-2) = е) 15 : (1/5)^(-3) =

Вычисляем:

а) \(9 \cdot 3^4 = 9 \cdot 81 = 729\) б) \(100 \cdot \left(-\frac{1}{5}\right)^{-2} = 100 \cdot (-5)^2 = 100 \cdot 25 = 2500\) в) \(3^{-1} + 2^{-3} = \frac{1}{3} + \frac{1}{8} = \frac{8}{24} + \frac{3}{24} = \frac{11}{24}\) г) \(0,2^0 - 0,1^{-3} = 1 - \left(\frac{1}{10}\right)^{-3} = 1 - 10^3 = 1 - 1000 = -999\) д) \(36 \cdot (-3)^{-2} = 36 \cdot \frac{1}{(-3)^2} = 36 \cdot \frac{1}{9} = 4\) е) \(15 : \left(\frac{1}{5}\right)^{-3} = 15 : 5^3 = 15 : 125 = \frac{15}{125} = \frac{3}{25}\)