Properties of a group question.

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Suppose G is a group and g,h are elements of g.

Does (g.h)n=gn.hn if we don't know what the groups operation is.
 
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In general, no. (gh)2= (gh)(gh) which, in a general group, is not the same as (gg)(hh)= g2h2. Of course, in a "commutative" group that would be true.
 
That is actually really obvious should have thought about it a little harder.

Thanks for the help.
 

Thread 'Finding the nth roots of a complex number'

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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