Only as a prefix operator; * has a pointer-related meaning for prefix and an arithmetic meaning for infix, there's no reason * * shouldn't be the same.

That'd be a syntactic ambiguity (in C-type languages) between "a * * b" being a to the power of b (i.e. "(a) * * (b)") or "a * * b" being a times the dereferencing of the pointer b (i.e. "(a) * (*b)"). You may be able to disambiguate this by prescedence, though it would be very ugly in the lexer (you could never have a STARSTAR token, it would have to be handled in the grammar) and would be terribly confusing.