Display 10^n as power

An alternative would be to define your own number form:

ClearAll[form]
SetAttributes[form, Listable]

form[x_] := ScientificForm[N@x, NumberFormat -> (Superscript[10, #3] &)]
form[1] := Superscript[10, 0]

10^Partition[Range[-6, 6], 7, 1] // form // 
   TableForm[#, TableHeadings -> {#[[4]], #[[4]]}] &

I hadnt seen Eldos answer before now, but I did copy the SetAttributes and ClearAll from him.

Define:

ClearAll[newForm]
SetAttributes[newForm, Listable]

newForm[x_] :=
  If[IntegerQ@x == True && Divisible[x, 10],
   ScientificForm[x // N,
    NumberFormat -> (
      If[Length@Characters@#3 != 0,
        If[ToExpression@#1 == 1,
         Row[{Superscript[10, 
            ToString[ToExpression@#3 - Length@Characters@#1 + 2]]}],
         Row[{x/10^(ToExpression@#3 - Length@Characters@#1 + 2), 
           "\[Times]", 
           Superscript[10, 
            ToString[ToExpression@#3 - Length@Characters@#1 + 2]]}]],
        #1] &)],
   ScientificForm[x]];

So the following comand gives a nice result

v = {1, 8^5, 130, 130., 15400000, 11.^7, 10^3};
newForm[v]

TableForm[
 Table[
  Superscript[10, x + y],
  {x, -3, 3},
  {y, -3, 3}
  ], TableHeadings -> {
   Table[Superscript[10, n], {n, -3, 3}],
   Table[Superscript[10, n], {n, -3, 3}]}
 ]