Let’s first define racism with this formula: Racism = racial prejudice + systemic institutional power
Ya, that's just a poor definition. It's the racial prejudice that's racism all on it's own.
It's true that if you have the systemic institutional power backing up your racism, it makes it much, much worse simply because your power gives you the ability to cause more harm than someone without power would be able to cause. That doesn't, however, mean that racial prejudice on the part of the powerless is any less racist. You can't just define groups out of the definition.
If a black person hates white people as a group, that black person is a racist. The fact that he does not have sufficient power to manifest his racism into the systematic oppression of the whites means that his racism isn't going to cause as much harm as that of someone who does have the power to oppress the group he hates, but it doesn't make him less of a racist.