Задание 5. Найдите значение выражения 1)-3-(-7,1)-2,8; 2)-0,4-(-10)²+54; 3) 91+0,3-(-10)³; 4) (1,3-10-2)-(6-10-3); 5) (5-103)2-(11-10-3); 6) (11-10-2)2-(15-103); 7)-0,7-(-10)3-9-(-10)2-51; 8) 0,009-9-900000; 9) 0,2-0,002-200; 10) -0,1-(-5)-2-(-5)3-16; 11) 7-10² +9-10°+8-10-3

Решение:

1. $$ -3 \cdot (-7.1) - 2.8 = 21.3 - 2.8 = 18.5 $$
2. $$ -0.4 \cdot (-10)^2 + 54 = -0.4 \cdot 100 + 54 = -40 + 54 = 14 $$
3. $$ 91 + 0.3 \cdot (-10)^3 = 91 + 0.3 \cdot (-1000) = 91 - 300 = -209 $$
4. $$ (1.3 \cdot 10^{-2}) \cdot (6 \cdot 10^{-3}) = 1.3 \cdot 6 \cdot 10^{-2} \cdot 10^{-3} = 7.8 \cdot 10^{-5} = 0.000078 $$
5. $$ (5 \cdot 10^3)^2 \cdot (11 \cdot 10^{-3}) = 5^2 \cdot (10^3)^2 \cdot 11 \cdot 10^{-3} = 25 \cdot 10^6 \cdot 11 \cdot 10^{-3} = 25 \cdot 11 \cdot 10^{6-3} = 275 \cdot 10^3 = 275000 $$
6. $$ (11 \cdot 10^{-2})^2 \cdot (15 \cdot 10^3) = 11^2 \cdot (10^{-2})^2 \cdot 15 \cdot 10^3 = 121 \cdot 10^{-4} \cdot 15 \cdot 10^3 = 121 \cdot 15 \cdot 10^{-4+3} = 1815 \cdot 10^{-1} = 181.5 $$
7. $$ -0.7 \cdot (-10)^3 - 9 \cdot (-10)^2 - 51 = -0.7 \cdot (-1000) - 9 \cdot 100 - 51 = 700 - 900 - 51 = -251 $$
8. $$ 0.009 \cdot 9 \cdot 900000 = 0.009 \cdot 900000 \cdot 9 = 9 \cdot 9000 = 81000 $$
9. $$ 0.2 - 0.002 \cdot 200 = 0.2 - 0.4 = -0.2 $$
10. $$ -0.1 \cdot (-5)^4 - 2 \cdot (-5)^3 - 16 = -0.1 \cdot 625 - 2 \cdot (-125) - 16 = -62.5 + 250 - 16 = 171.5 $$
11. $$ 7 \cdot 10^1 + 9 \cdot 10^0 + 8 \cdot 10^{-3} = 7 \cdot 10 + 9 \cdot 1 + 8 \cdot 0.001 = 70 + 9 + 0.008 = 79.008 $$

Ответ: 1) 18.5; 2) 14; 3) -209; 4) 0.000078; 5) 275000; 6) 181.5; 7) -251; 8) 81000; 9) -0.2; 10) 171.5; 11) 79.008