Решим данные примеры:
а) $$-3^3 \cdot 4^{-2} = -27 \cdot \frac{1}{4^2} = -27 \cdot \frac{1}{16} = -\frac{27}{16} = -1 \frac{11}{16}$$
б) $$(-10)^{-4} \cdot 7^2 = \frac{1}{(-10)^4} \cdot 49 = \frac{1}{10000} \cdot 49 = \frac{49}{10000} = 0,0049$$
в) $$\left(-\frac{3}{5}\right)^{-1} + 3^{-2} = -\frac{5}{3} + \frac{1}{3^2} = -\frac{5}{3} + \frac{1}{9} = -\frac{15}{9} + \frac{1}{9} = -\frac{14}{9} = -1 \frac{5}{9}$$
г) $$(-3)^{-3} + (-6)^{-2} = \frac{1}{(-3)^3} + \frac{1}{(-6)^2} = -\frac{1}{27} + \frac{1}{36} = -\frac{4}{108} + \frac{3}{108} = -\frac{1}{108}$$
д) $$(-0,5)^{-2} - (-1)^{-7} = \left(-\frac{1}{2}\right)^{-2} - (-1)^{-7} = (-2)^2 - \frac{1}{(-1)^7} = 4 - \frac{1}{-1} = 4 - (-1) = 4 + 1 = 5$$
е) $$10^{-3} + (-0,1)^{-4} = \frac{1}{10^3} + \left(-\frac{1}{10}\right)^{-4} = \frac{1}{1000} + (-10)^4 = \frac{1}{1000} + 10000 = 0,001 + 10000 = 10000,001$$
Ответы:
а) -1 11/16
б) 0,0049
в) -1 5/9
г) -1/108
д) 5
е) 10000,001