Grow ponytail palm in bright light for best growth, but it tolerates medium- and low-light spots, as well. Because it stores water in its thick trunk, ponytail palm can survive extended periods with no water -- making it the perfect houseplant if you tend to travel a lot or are a forgetful waterer. That said, this houseplant tree will grow best if watered regularly -- when the top inch or so of the potting mix starts to dry.