I'm trying to understand an answer to the question: http://mathematica.stackexchange.com/questions/65471/how-to-do-algebra-on-summations-of-variable-expressions/65576
The following input:

    reindex = s : sum[_, {i_, __}] :> (s /. i -> Unique[ToString[i]]);
    unpower = s_sum^p_Integer :> Times @@ Table[s /. reindex, {p}];
    test = (5*sum[x[k], {k, 1, kk}])^2;
    test /. unpower
    
    Out[4]= 25 sum[x[k3], {k3, 1, kk}] sum[x[k4], {k4, 1, kk}]

produces result, that differs from result produced by expressions ($25\neq625$):

    unpowerstep1 = s_sum^p_Integer :> Table[s /. reindex, {p}];
    intermediate = test /. unpowerstep1
    Times @@ intermediate

    Out[6]= {25 sum[x[k5], {k5, 1, kk}], 25 sum[x[k6], {k6, 1, kk}]}    
    Out[7]= 625 sum[x[k5], {k5, 1, kk}] sum[x[k6], {k6, 1, kk}]

Also, I cannot undestand what `s_sum` mean. Does it mean, that s is any expression with head sum?