reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem NEWTON027:
  for t,z be Integer holds
    t|^n gcd z|^n = (t gcd z)|^n
  proof
    let t,z be Integer;
    A1: t|^n gcd z|^n = |.t|^n.| gcd |.z|^n.|
    & t gcd z = |.t.| gcd |.z.| by INT_2:34;
    |.t|^n.| = |.t.||^n & |.z|^n.| = |.z.||^n by TAYLOR_2:1;
    hence thesis by A1, NEWTON02:7;
  end;
