Question

Дам 30 балов за решение, пожалуйста напишите подробно

Answer 1

1)
5^8 * 2^6 / 10^7 = 5^8 * 2^6 / (5^7 * 2^7) = 5/2 = 2.5

2)
3^(1/3) = (81^(1/4))^(1/3) = 81^(1/12),
3^(1/3) / 3^(1/12) = (81 / 3)^(1/12) = ((3^3)^(1/3))^(1/4) = 3^(1/4)
3^(1/3) * 4^(1/4) / 3^(1/12) = 3^(1/4) * 4^(1/4) = 12^(1/4)

3)
x^5 * x^6 / x^9 = x^11 / x^9 = x^2 = {x = 12} = 144

4)
f(y) = (2y - 3/y)(3y - 2/y)
f(1/y) = (2/y - 3y)(3/y - 2y) = (-1)^2 * (2y - 3/y)(3y - 2/y) = f(y)
f(y)/f(1/y) = 1

5)
sin^2(125 град) = sin^2(90 + 35) = cos^2(35)
8 / (sin^2(35) + cos^2(35)) = 8/1 = 8

6)
cos(2x) = cos^2(x) - sin^2(x) = cos^2(x) - (1 - cos^2(x)) = 2cos^2(x) - 1 = {cosx = 1/4) = 2/16 - 1 = -7/8
4cos2x = -7/2 = -3.5