Analysis: Thm 1.21 and Question from Walter Rudin

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And what? Surely you don't just want the answer handed to you (and we won't do that even if you do). What have you tried with these? In particular, what is the definition of a^{1/n} for a a positive real number and n an integer?
 
Im sorry. I forgot I had posted it in a hurry. Just part a here.
 
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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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