Yes that is exactly correct, they all multiply together. Iron Fist is 20% extra (x1.2) and STAB is 50% extra (x1.5).
So the power would be 150 x 1.2 x 1.5 = 270
You could also hold an item like Fist Plate for another 20% extra (324 total) or Fighting Gem for 50% extra on the first move (405 total)!!