The reason we use ECC multiplication (which I'm sure you know is not just regular integer multiplication) is that it is a homomorphic trapdoor function.
You could potentially use unpadded RSA to achieve the same objective https://en.wikipedia.org/wiki/Homomorphic_encryption
However, the reason that all cryptocurrencies use ECC and not RSA is that RSA public keys in particular are enormous compared to the size of ECC public keys. RSA would make for an unnecessarily bloated blockchain.
There is another way of interpreting your question though. Sometimes people use the term exponentiation to describe the exact same operation that Monero usually describes as scalar multiplication. In which case, you could use the alternate notation. Just note that the equivalent of
rA is written as
A^r and not