What are the incorrect limits on the integral in this random variables problem?

vabamyyr
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Since I am noob in LaTex then ill post a document in Word.
 

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The limits on your integral are incorrect. You have to divide the x range into 2 parts (0,z) and (z,1). For the first part the y range is (0,1). For the second part the y range is (0,z/x). The point being that y has an upper limit of min(1,z/x).
 
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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