Retina, 3 bytes

.
1

Try it online!

Takes inputs separated by space (or any single non-newline character)

Replaces all digits with 1, and joins the resulting numbers with another 1. I couldn't find a counterexample, but I don't have a proof of correctness, so any help is appreciated :)

Retina, 3 bytes

.
1

Try it online!

Takes inputs separated by space (or any single non-newline character)

Replaces all digits with 1, and joins the resulting numbers with another 1.

Proof of correctness

Courtesy of Martin Ender

• This operation computes a result with one more digit than the number of digits of the two numbers together; the only operation that could produce a result so big is exponentiation.

• The result is a repunit (a number whose digits are all 1).

• "It is know [sic] [...] that a repunit in base 10 cannot [...] be a perfect power." This means that this result can't be produced by exponentiation either.