Abstract Algebra Please explain and show all steps. Let ( a ) and ( b ) be elements of an abelian group ( G ). Prove that for any positive integer ( n ), we have ( (a b)^{n}=a^{n} b^{n} ). Is this true for non-abelian groups? (If so, prove it; otherwise give one counterexample.) Remark: First prove this is true for any non-nega

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Abstract Algebra  Please explain and show all steps.  Let  ( a  ) and  ( b  ) be elements of an abelian group  ( G  ). Prove that for any positive integer  ( n  ), we have  ( (a b)^{n}=a^{n} b^{n}  ). Is this true for non-abelian groups? (If so, prove it; otherwise give one counterexample.) Remark: First prove this is true for any non-negative integer  ( n  ). Then, use properties of inverses to extend this for negative values of  ( n  ).

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