Find a Regular Expression to describe the following language: {b, a, abc, ab, a²bc², ab², ..., aⁿbcⁿ, abⁿ, ...}

I am studying for a discrete math class, and we are currently learning about Regular Languages, Regular Expressions, and Finite Automata.

I am stuck on this problem because I don't know how to get the same number of "a" and "c" with a "b" in between, in the expression aⁿbcⁿ. At first, I was thinking the expression a*bc* would match, but I think since they are both raised to "n," this means they have to have the same number of a's and c's, which I can't find a way of doing.

A friend of mine who had the class a year ago said this might actually be a trick question, and that this is meant to showcase a limitation of the regular expressions, but he also said that he wasn't sure since it has been a long time since he took the class.

Please explain how you came up with the Regular Expression that matches this language, or if there is not one, please explain why. I would like to gain a deeper understanding of Regular Expressions, and be able to do more problems similar to this in the future. Thanks!