C++ FAQ Celebrating Twenty-One Years of the C++ FAQ!!!
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Section 13:
[13.7] Can I create a operator** for "to-the-power-of" operations?

Nope.

The names of, precedence of, associativity of, and arity of operators is fixed by the language. There is no operator** in C++, so you cannot create one for a class type.

If you're in doubt, consider that x ** y is the same as x * (*y) (in other words, the compiler assumes y is a pointer). Besides, operator overloading is just syntactic sugar for function calls. Although this particular syntactic sugar can be very sweet, it doesn't add anything fundamental. I suggest you overload pow(base,exponent) (a double precision version is in <cmath>).

By the way, operator^ can work for to-the-power-of, except it has the wrong precedence and associativity.