Does Python optimize low-power functions?

[John Ladasky]

The following two functions return the same result:

    x**2
    x*x

But they may be computed in different ways.  The first choice can accommodate non-integer powers and so it would logically proceed by taking a logarithm, multiplying by the power (in this case, 2), and then taking the anti-logarithm.  But for a trivial value for the power like 2, this is clearly a wasteful choice.  Just multiply x by itself, and skip the expensive log and anti-log steps.

My question is, what do Python interpreters do with power operators where the power is a small constant, like 2?  Do they know to take the shortcut?