+0  
 
-2
41
2
avatar+816 

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

 Aug 10, 2023
 #1
avatar
+1

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)

 Aug 10, 2023
 #2
avatar+129433 
+1

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

 

cool cool cool

 Aug 10, 2023

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