reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;

theorem
  exp(K*`M,N) = exp(K,N)*`exp(M,N)
proof
  card(K*`M) = K*`M & card N = card N;
  hence exp(K*`M,N) = card Funcs(N,[:K,M:]) by FUNCT_5:61
    .= card [:Funcs(N,K),Funcs(N,M):] by FUNCT_5:64
    .= exp(K,N)*`exp(M,N) by Th6;
end;
