I've been training my dad for about six years, and amongst the grumbles I get for "going too hard on him," I have watched his balance, strength and mobility transform in that time.
There are some essential strength exercises I add to his routine (in various forms) regularly, but we often work on his mobility twice a week. We try to stay as low on equipment as we can, but for the exercise I'm sharing with you, you don't need anything except a resistance band, but even that's optional.