My date has some black powder in it. Is it safe to eat?

What you're looking at is mold, not uncommon in dates and figs, and not a recommended snack. Not only does it have an unpleasant taste, it may trigger an allergic response in some individuals.

Whole Fresh Dates in Yuma, Arizona (USA) gives a good overview in its August 6, 2016, blog:

What is this in my Date?

The unfortunate truth for many date lovers and fig lovers too is that these deliciously tasting fruits are susceptible to being tainted by bugs and black mold. This is a side of the date industry that is not talked about all that much, and for good reason. Nobody likes talking about nasty critters or black unknown powdery stuff in their food. We will try and bring some clarity to this problem as well as some things you can do to ensure you are not biting into a date that might contain some foreign elements.

What's the Black Mold in Dates?

The perfect environment for growing dates are hot extremely dry climates that receive very little rain fall. Moisture is a killer for date crops. And this black dust is exactly that, it's excessive moisture that has caused the date to turn. ... Actually, date fruits growing on date cluster need several days of 100 degree weather to ensure proper development and reduce the likelihood of moisture.... Simply put, dry growing conditions equals less moisture for mold to exist, wet environment equals black dust (mold).

Here's What YOU Can Do:

Those that have eaten dates for sometime know that you just don't bite into a date. You need to peel it apart and open it up. Always open your dates prior to biting into them. This is a process that all date lovers either know or have learned over the years of eating dates. I typically will pick out several dates that I'm going to eat slice long ways from the top of the date toward the bottom. Split it open, remove the date and then wash thoroughly regardless if I see anything or not.