The statement is ambiguous.
If collective intelligence can have the attribute of power then diversity and collective intelligence can both be objects of preposition of.
If collective intelligence cannot have the attribute of power, then the power of diversity and collective intelligence are the objects of preposition in.
The meaning would involve a semantic decision.
She believes in the veracity of his remarks and three square meals.
The statement is grammatical but odd on a semantic level since it involves two somewhat different meanings of believe in, one meaning for the first object and another for the second object. Also, three square meals cannot have the attribute of veracity.
If the meaning of the verb is the same for both objects, and both objects can have the attribute in question, as in your examples, then there is no such oddity. But it is not absolutely clear that the attribute power applies to both, and you would have to repeat power if absolute clarity was your goal and you did not want to change the sentence structure.
If your question isn't merely of an academic nature and you're looking for writing strategies, you could rephrase the sentence in any number of ways. Here's one:
She believes diversity and collective intelligence are both powerful.