Mann Whitney U Test: Determining "First" Population

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The question relate to the Mann Whitney U test with two populations.

For the test statistic formula, there is a R1 term, which is the sum of the ranks of the "first" population. My question is, given any two populations, how do i decide which one is the "first" population?
 
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The Mann Whitney U test essentially tests the absolute value of the difference in means of two populations. It doesn't matter which is the "first" and which is the "second" population.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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