1.17. Найдите значения выражений 10а², (10a)², -10а², (-10a)², 10а³, (10a)³, -10а³ и (-10a)³ при: a) a = 10; б) a = -1; в) a = 1/2; г) a = -0,2.

Решение:

а) a = 10

• $$10a^2 = 10 imes 10^2 = 10 imes 100 = 1000$$
• $$(10a)^2 = (10 imes 10)^2 = 100^2 = 10000$$
• $$-10a^2 = -10 imes 10^2 = -10 imes 100 = -1000$$
• $$(-10a)^2 = (-10 imes 10)^2 = (-100)^2 = 10000$$
• $$10a^3 = 10 imes 10^3 = 10 imes 1000 = 10000$$
• $$(10a)^3 = (10 imes 10)^3 = 100^3 = 1000000$$
• $$-10a^3 = -10 imes 10^3 = -10 imes 1000 = -10000$$
• $$(-10a)^3 = (-10 imes 10)^3 = (-100)^3 = -1000000$$

б) a = -1

• $$10a^2 = 10 imes (-1)^2 = 10 imes 1 = 10$$
• $$(10a)^2 = (10 imes -1)^2 = (-10)^2 = 100$$
• $$-10a^2 = -10 imes (-1)^2 = -10 imes 1 = -10$$
• $$(-10a)^2 = (-10 imes -1)^2 = (10)^2 = 100$$
• $$10a^3 = 10 imes (-1)^3 = 10 imes (-1) = -10$$
• $$(10a)^3 = (10 imes -1)^3 = (-10)^3 = -1000$$
• $$-10a^3 = -10 imes (-1)^3 = -10 imes (-1) = 10$$
• $$(-10a)^3 = (-10 imes -1)^3 = (10)^3 = 1000$$

в) a = 1/2

• $$10a^2 = 10 imes (rac{1}{2})^2 = 10 imes rac{1}{4} = rac{10}{4} = rac{5}{2}$$
• $$(10a)^2 = (10 imes rac{1}{2})^2 = 5^2 = 25$$
• $$-10a^2 = -10 imes (rac{1}{2})^2 = -10 imes rac{1}{4} = -rac{10}{4} = -rac{5}{2}$$
• $$(-10a)^2 = (-10 imes rac{1}{2})^2 = (-5)^2 = 25$$
• $$10a^3 = 10 imes (rac{1}{2})^3 = 10 imes rac{1}{8} = rac{10}{8} = rac{5}{4}$$
• $$(10a)^3 = (10 imes rac{1}{2})^3 = 5^3 = 125$$
• $$-10a^3 = -10 imes (rac{1}{2})^3 = -10 imes rac{1}{8} = -rac{10}{8} = -rac{5}{4}$$
• $$(-10a)^3 = (-10 imes rac{1}{2})^3 = (-5)^3 = -125$$

г) a = -0,2 = -1/5

• $$10a^2 = 10 imes (-rac{1}{5})^2 = 10 imes rac{1}{25} = rac{10}{25} = rac{2}{5}$$
• $$(10a)^2 = (10 imes -rac{1}{5})^2 = (-2)^2 = 4$$
• $$-10a^2 = -10 imes (-rac{1}{5})^2 = -10 imes rac{1}{25} = -rac{10}{25} = -rac{2}{5}$$
• $$(-10a)^2 = (-10 imes -rac{1}{5})^2 = (2)^2 = 4$$
• $$10a^3 = 10 imes (-rac{1}{5})^3 = 10 imes (-rac{1}{125}) = -rac{10}{125} = -rac{2}{25}$$
• $$(10a)^3 = (10 imes -rac{1}{5})^3 = (-2)^3 = -8$$
• $$-10a^3 = -10 imes (-rac{1}{5})^3 = -10 imes (-rac{1}{125}) = rac{10}{125} = rac{2}{25}$$
• $$(-10a)^3 = (-10 imes -rac{1}{5})^3 = (2)^3 = 8$$

Ответ:

a) a = 10

1000; 10000; -1000; 10000; 10000; 1000000; -10000; -1000000.

б) a = -1

10; 100; -10; 100; -10; -1000; 10; 1000.

в) a = 1/2

5/2; 25; -5/2; 25; 5/4; 125; -5/4; -125.

г) a = -0,2

2/5; 4; -2/5; 4; -2/25; -8; 2/25; 8.