1.
а) 2 * 2^(-3) = 2 * 1/(2^3) = 2 * (1/8) = 2/8 = 1/4
б) (1/4)^(-2) * 4 = (4/1)^2 * 4 = 4^2 * 4 = 16 * 4 = 64
в) [( 3^(-2) )^3 * 27^2]/3 = [( 1/(3^2) )^3 * 27*27]/3 = [( 1/9 )^3 * 27 * 27]/3 = [(1/(9^3)) * 9*3 * 9*3]/3 = [(1/(9 * 9)) * 9 * 9 * 3 * 3]/3 = || сокращаем 9/9, 9/9 и 3/3 || = 3
2.
а) 5 * 16^(1/4) - 0,2 * (-0,027)^(1/3) + 1^(1/5) = 5 * (2^3)^(1/3) - 0,2 * ((-0,3)^3)^(1/3) + 1 = 5 * 2 - 0,2 * (-0,3) + 1 = 10 - (-0,06) + 1 = 11 + 0,06 = 11,06
б) (243^(1/4))/(3^(1/4)) = (243/3)^(1/4) = 81^(1/4) = (3^4)^(1/4) = 3
в) (0,00001 * 32)^(1/5) = ((0,1 * 2)^5)^(1/5) = 0,1 * 2 = 0,2
г) (5^(1/3))^(-1/12) = 1 / (5^(1/3))^12 = 5^(12/3) = 5^4 = 25*25 = 625
4.
2 * (a^(1/2))^(1/3) + ((ab)^(1/6))/(b^(1/6)) = 2 * a^(1/6) + a^(1/6) * (b^(1/6) / b^(1/6)) = 2 * a^(1/6) + a^(1/6) = 3 * a^(1/6)
5.
(3+5^(1/2))^(1/4) * (3-5^(1/2))^(1/4) = [(3+5^(1/2)) * (3-5^(1/2))]^(1/4) = || по свойству (a+b)(a-b)=a^2-b^2 || = [3^2 - 5]^(1/4) = [9 - 5]^(1/4) = 4^(1/4) = (2^2)^(1/4) = 2^(2/4) = 2^(1/2)