+817 Arrange the following numbers in increasing order (smallest first, biggest last)
A = 2^(1/2)*4^(1/6)
B = (128)^(1/12)/64^(1/3)
C = (8^(1/5))^(2^2)
D = sqrt(4/(2*8*4))
E = (2^(1/4)*4^(-1/2))^3
A = 2^(1/2)*4^(1/6) =1.781797436
B = (128)^(1/12)/64^(1/3)=0.3745767692
C = (8^(1/5))^(2^2)=5.278031643
D = sqrt(4/(2*8*4))=1 / 4
E = (2^(1/4)*4^(-1/2))^3=0.2102241038
Sorted from smallest to largest:
(E=0.2102241038, D=0.25, B=0.3745767692, A=1.781797436, C=5.278031643)
+129771 A = 2^(1/2) * 4^(1/6) = 2^(1/2)*(2^2)^(1/6) = 2^(1/2)* 2^(2/6) = 2^(3/6)*2^(2/6) = 2^(5/6) = 2^(10/12)
B = (128)^(1/12) / 64^(1/3) = (2^7)^(1/12) / (2^6)^(1/3) = 2^(7/12) / 2^(2) = 2^(7/12) / 2^(24/12) = 2^(-17/12)
C = (8^(1/5))^(2^2) = 8^(1/5)^4 = (2^3)^(4/5) = 2^(12/5)
D = sqrt (4/ (2*8*4)) = sqrt (4/64) = sqrt (1/16) = (1/16)^(1/2) = 1/4 = 1/2^2 = 2^(-2) = 2^(-24/12)
E= (2^(1/4)*4^(-1/2))^3 = (2^(1/4) *(2^(2))^(-1/2))^3 = (2^(1/4)*2^(-1))^3 = (2^(-3/4))^3 = 2^(-9/4) = 2^(-27/12)
E , D, B , A , C
