Finding a finite automata that accepts a language that is the combination of two other languages with their own automata


I’m told that we have two DFA one A and one B both on alphabet $ \sum$ .

I’m then told to define a DFA (5-tuple representation) with this condition {w | w = $ a_i b_i$ $ a_k b_k$ and all the $ a \in A$ and all the $ b \in B$ }

Also 1 $ \leq$ i $ \leq$ k and $ a_i \in \sum$ and $ b_i \in \sum$ .

However I simply do not understand how I’m supposed to do this. Simply put my confusion is what $ w = a_i b_i$ mean. Is it concatenation? Does it mean that the word $ w$ is the concatenation of a with b?