Can one partially apply the second argument of a function that takes no keyword arguments?

No

According to the documentation, partial cannot do this (emphasis my own):

partial.args

The leftmost positional arguments that will be prepended to the positional arguments

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You could always just "fix" pow to have keyword args:

_pow = pow
pow = lambda x, y: _pow(x, y)

I think I'd just use this simple one-liner:

import itertools
print list(itertools.imap(pow, [1, 2, 3], itertools.repeat(2)))

Update:

I also came up with a funnier than useful solution. It's a beautiful syntactic sugar, profiting from the fact that the ... literal means Ellipsis in Python3. It's a modified version of partial, allowing to omit some positional arguments between the leftmost and rightmost ones. The only drawback is that you can't pass anymore Ellipsis as argument.

import itertools
def partial(func, *args, **keywords):
    def newfunc(*fargs, **fkeywords):
        newkeywords = keywords.copy()
        newkeywords.update(fkeywords)
        return func(*(newfunc.leftmost_args + fargs + newfunc.rightmost_args), **newkeywords)
    newfunc.func = func
    args = iter(args)
    newfunc.leftmost_args = tuple(itertools.takewhile(lambda v: v != Ellipsis, args))
    newfunc.rightmost_args = tuple(args)
    newfunc.keywords = keywords
    return newfunc

>>> print partial(pow, ..., 2, 3)(5) # (5^2)%3
1
>>> print partial(pow, 2, ..., 3)(5) # (2^5)%3
2
>>> print partial(pow, 2, 3, ...)(5) # (2^3)%5
3
>>> print partial(pow, 2, 3)(5) # (2^3)%5
3

So the the solution for the original question would be with this version of partial list(map(partial(pow, ..., 2),xs))

Why not just create a quick lambda function which reorders the args and partial that

partial(lambda p, x: pow(x, p), 2)