1.19. Выполните действия: a) 1⁹ - (-1)⁹; б) (-2³)² - 1⁶; в) -10² · 0,3; г) (-31/3)³ · 0,027; д) -3² · (-2/3)² - 0,5²; e) -4² · 1/24 + 1; ж) (-3 · (-2/3)²) - 0,5²; 3) (-31/3)³ + (-3)³; и) (1 - 4/27 · (-3)²)³; к) -5 · ((-2/3)² - (1/3)²).

Решение:

1. 1⁹ - (-1)⁹: $$1^9 = 1$$. $$(-1)^9 = -1$$. $$1 - (-1) = 1 + 1 = 2$$.
2. (-2³)² - 1⁶: $$(-2^3) = -8$$. $$(-8)^2 = 64$$. $$1^6 = 1$$. $$64 - 1 = 63$$.
3. -10² · 0,3: $$-10^2 = -100$$. $$-100 imes 0.3 = -30$$.
4. (-3¹/₃)³ · 0,027: $$-3rac{1}{3} = -rac{10}{3}$$. $$(-rac{10}{3})^3 = -rac{1000}{27}$$. $$0.027 = rac{27}{1000}$$. $$(-rac{1000}{27}) imes rac{27}{1000} = -1$$.
5. -3² · (-2/3)² - 0,5²: $$-3^2 = -9$$. $$(-rac{2}{3})^2 = rac{4}{9}$$. $$-9 imes rac{4}{9} = -4$$. $$0.5^2 = 0.25 = rac{1}{4}$$. $$-4 - rac{1}{4} = -rac{16}{4} - rac{1}{4} = -rac{17}{4} = -4.25$$.
6. -4² · 1/24 + 1: $$-4^2 = -16$$. $$-16 imes rac{1}{24} = -rac{16}{24} = -rac{2}{3}$$. $$-rac{2}{3} + 1 = rac{1}{3}$$.
7. -3 · (-2/3)² - 0,5²: $$(-rac{2}{3})^2 = rac{4}{9}$$. $$-3 imes rac{4}{9} = -rac{12}{9} = -rac{4}{3}$$. $$0.5^2 = rac{1}{4}$$. $$-rac{4}{3} - rac{1}{4} = -rac{16}{12} - rac{3}{12} = -rac{19}{12}$$.
8. (-3¹/₃)³ + (-3)³: $$-3rac{1}{3} = -rac{10}{3}$$. $$(-rac{10}{3})^3 = -rac{1000}{27}$$. $$(-3)^3 = -27$$. $$-rac{1000}{27} - 27 = -rac{1000}{27} - rac{729}{27} = -rac{1729}{27}$$.
9. (1 - 4/27 · (-3)²)³: $$(-3)^2 = 9$$. $$rac{4}{27} imes 9 = rac{36}{27} = rac{4}{3}$$. $$1 - rac{4}{3} = -rac{1}{3}$$. $$(-rac{1}{3})^3 = -rac{1}{27}$$.
10. -5 · ((-2/3)² - (1/3)²): $$(-rac{2}{3})^2 = rac{4}{9}$$. $$(rac{1}{3})^2 = rac{1}{9}$$. $$rac{4}{9} - rac{1}{9} = rac{3}{9} = rac{1}{3}$$. $$-5 imes rac{1}{3} = -rac{5}{3}$$.

Ответ: 2; 63; -30; -1; -4.25; 1/3; -19/12; -1729/27; -1/27; -5/3.