Constructive Proof on Regular Languages
In general, the answer is usually "no". Equality of languages is, most of the time, undecidable; regular languages are a special case here, at least when they are given in certain representations.

What you can do is to break down those languages in terms of closure properties of REG, e.g. reversal, homomorphism, complement, etc.

Since your task here is to prove such closure properties, you'll have to take the long and creative route: come up with a construction and prove it correct. The purpose of the exercise is to train doing exactly that, so taking a shortcut would be unwise.