No need to buy fancy vacuum-packed bags for space-saving packing. Use one gallon-sized Ziploc bag for underwear, another for bras, and another for socks.
Fold (or roll) the items and put them in the bags (I can fit a week’s worth of each in one bag). When all items are in the bag, squeeze to force the air out, and zip it.
I put these in the lid portion of my suitcase, so security sees the bags clearly if they open my suitcase. Of course, an added benefit is that my things take up much less room than they otherwise would.