Can you mix baking powder and baking soda?

There is no need to. Baking powder has baking soda in it already. Baking powder is a mixture of cream of tartar and baking soda. Adding extra soda to it might make the bake good you are preparing come out with "unexpected" results. If a recipe actually calls for it, fine, but I have never seen one that calls for both.

If you don't have enough of one or the other for you recipe, you can mix them but if you're low on soda, the baked good may not rise as much. It's best to follow the amounts in the recipe since each one responds a little differently depending on the acid content of the batter.