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What are you taking the limit to? What messages or behavior do you see when evaluating this?

If Mathematica only repeats back the input you gave it, then that means that Limit was not able to find a value for the limit you mentioned. Perhaps to solve the problem, certain assumptions have to be made about the values of a, b, x, and y? If so you can use the Assumptions option for Limit. See examples in the documentation for how to use this optional argument to Limit.

For example, Mathematica will not be able to find a value for Limit[(b y^r)^(1/r), r -> Infinity], but if you let it know that y is greater than 0, it will be able to find a result:

Limit[(b y^r)^(1/r), r -> \[Infinity], Assumptions -> {0 < y}]