Вариант № 2. № 1. Вычислите: 1) 11⁻²; 2) 6⁻³; 3) (-5)⁻⁴; 4) (-4)⁻³; 5) (-9/5)⁻¹; 6) (5/7)⁻³; 7) (2/5)⁻²; 8) (1 1/4)⁻¹; 9) 0,7⁻²; 10) 1,2⁻²; № 2. Найдите значение выражения: 1) 5⁻² + 10⁻³; 2) (6/7)⁻¹ + 6⁻² - (-3,5)⁰; 3) (9/4)⁻² * 2⁻⁵.

№ 1. Вычислите:

1. $$11^{-2} = \frac{1}{11^2} = \frac{1}{121}$$
2. $$6^{-3} = \frac{1}{6^3} = \frac{1}{216}$$
3. $$(-5)^{-4} = \frac{1}{(-5)^4} = \frac{1}{625}$$
4. $$(-4)^{-3} = \frac{1}{(-4)^3} = -\frac{1}{64}$$
5. $$\left(-\frac{9}{5}\right)^{-1} = -\frac{5}{9}$$
6. $$\left(\frac{5}{7}\right)^{-3} = \left(\frac{7}{5}\right)^3 = \frac{7^3}{5^3} = \frac{343}{125} = 2\frac{93}{125}$$
7. $$\left(\frac{2}{5}\right)^{-2} = \left(\frac{5}{2}\right)^2 = \frac{5^2}{2^2} = \frac{25}{4} = 6\frac{1}{4}$$
8. $$\left(1\frac{1}{4}\right)^{-1} = \left(\frac{5}{4}\right)^{-1} = \frac{4}{5}$$
9. $$0,7^{-2} = \left(\frac{7}{10}\right)^{-2} = \left(\frac{10}{7}\right)^2 = \frac{100}{49} = 2\frac{2}{49}$$
10. $$1,2^{-2} = \left(\frac{12}{10}\right)^{-2} = \left(\frac{6}{5}\right)^{-2} = \left(\frac{5}{6}\right)^2 = \frac{25}{36}$$

№ 2. Найдите значение выражения:

1. $$5^{-2} + 10^{-3} = \frac{1}{5^2} + \frac{1}{10^3} = \frac{1}{25} + \frac{1}{1000} = \frac{40}{1000} + \frac{1}{1000} = \frac{41}{1000} = 0,041$$
2. $$\left(\frac{6}{7}\right)^{-1} + 6^{-2} - (-3,5)^0 = \frac{7}{6} + \frac{1}{6^2} - 1 = \frac{7}{6} + \frac{1}{36} - 1 = \frac{42}{36} + \frac{1}{36} - \frac{36}{36} = \frac{7}{36}$$
3. $$\left(\frac{9}{4}\right)^{-2} \cdot 2^{-5} = \left(\frac{4}{9}\right)^2 \cdot \frac{1}{2^5} = \frac{4^2}{9^2} \cdot \frac{1}{32} = \frac{16}{81} \cdot \frac{1}{32} = \frac{1}{81 \cdot 2} = \frac{1}{162}$$