Yes probiotics and prebiotics should be taken together which makes both the probiotics and prebiotics more effective.
You can take probiotics without taking prebiotics and they will still work just fine.
However when taken together the probiotics and prebiotics work much better.
This is known as microbiome therapy and is commonly used by people taking the probiotics and prebiotics.
I take both probiotics and prebiotics together myself and they are much more effective when I do so.
I asked my doctor if I should take them together and she said that it would be a good idea to make them work better but they would work fine without each other.