put these numbers into ascending order..?

2^5/6, 4^2/3, 8^1/2,32^1/3 

This isn't as hard as it seems if we can write them in a little different mannner.....

8^1/2      =   [2³]^1/2   = 2^3/2     =  2^9/6

4^2/3   =   [2²]^2/3  = 2^4/3    =  2^8/6

32^1/3  =  [2⁵]^1/3  = 2^5/3     = 2 ^10/6

2^5/6           =   [2]^5/6     =  2^5/6    

And  since     10/6 > 9/6 > 8/6  > 5/6

Then     2 ^10/6  > 2^9/6 > 2^8/6  > 2^5/6   

So....in ascending order, we have

2^5/6 ,  4^2/3,  8^1/2, 32^1/3

2^5/6,  4^2/3,  8^1/2,  32^1/3,