Naming

This operator is called "power" in the ISO standard of 1995, page 119.

More on operators:

As Wouter Beek says:

Notice that the precedence of (**)/2 is xfx, which is different from that of (^)/2, which is xfy.

These operators also have the same precedence, 200 (pretty strong), same as the precedence of unary -. (see op/3)

?- write_canonical( (Y = 2, X is 2 ** (-Y)) ).
','(=(A,2),is(_,**(2,-(A))))

What's interesting is that ** must be "alone" in a non-parenthesized expression (the operator is xfx, non-associative), whereas ^ can chain, associating to the right (the operator is xfy, right-associative):

?- write_canonical( x ** y ** z ).
ERROR: Syntax error: Operator priority clash

?- write_canonical( x ** (y ** z) ).
**(x,**(y,z))

But:

?- write_canonical( x ^ y ^ z ).
^(x,^(y,z))
true.

=Notice that the precedence of (**)/2 is xfx, which is different from that of (^)/2, which is xfy.

This may lead to surprises such as the following succeeding:

?- Y = 2, X is 2 ^ -Y.
Y = 2,
X = 0.25.

while the following throws an exception:

?- Y = 2, X is 2 ** -Y.
ERROR: Syntax error: Operator priority clash
ERROR: Y = 2, X is 2 *
ERROR: ** here **
ERROR: * -Y .

The introduction of brackets in the exponent of (**)/2 solves this.=