Learn Finnish: Jos sinulla on valtaa, voit hallita mitä tahansa. - If you have power, you can rule anything.

The pronoun mikä has to match the case required by the rest of the sentence. The verb hallita (to rule, to control) requires its object to be in the partitive case. Therefore, the base word mikä becomes the partitive mitä, followed by the unchanging word tahansa.

Could I use kaikkea instead of mitä tahansa in this sentence?

You could, but it changes the meaning slightly. Voit hallita kaikkea means 'you can rule everything', whereas voit hallita mitä tahansa emphasizes free choice, meaning 'you can rule anything (at all)' or 'whatever you want'.

Why is valtaa in the partitive case in the first clause?

In Finnish 'have' structures like sinulla on (you have), if the thing being possessed is an abstract concept or an uncountable mass noun like valta (power), it must be in the partitive case (valtaa).

Does hallita only mean 'to rule' in a political sense?

While it does mean 'to rule' or 'to govern', hallita is also very commonly used in everyday contexts to mean 'to control', 'to manage', or 'to master' (such as mastering a new skill). In all these senses, it takes a partitive object.