Beaucarnea recurvata is not a palm. It is related to Agave and Yucca, and the swollen base of the trunk is a water store that lets it survive long droughts.
That base is called a caudex, and it is why the plant tolerates so much neglect.
What every Ponytail Palm wants
Bright light, including direct sun. This is one of the few common houseplants that is happier on a south-facing windowsill than off it.
Water thoroughly, then leave it until the soil is completely dry throughout. Every three to four weeks in summer and considerably less in winter.
Use a gritty, free-draining mix and a pot that is not too large. Wet soil around the caudex causes it to soften and rot, and there is no recovering from that.
Ponytail Palms are non-toxic to cats and dogs.