I am a salary employee who gets paid for a 80hr pay period. In that 80 hr period I took 16hrs vacation time. On my check I got paid for my vacation time,but I was short 8hrs pay for my regular time. Their reason for the short was the one week I did 40 hrs in 4 days instead of 5 days. My question is,is that legal for them not to pay me for my regular hrs even though they were done in 4 days instead of 5?

What country are you in? Salary has nothing to do with the hours worked. However, unless they have agreed to give you a day off you have to be docked for not working that 5th day. You are supposed to report to work everyday, somedays more than 8 hours and maybe some less, but still you must report to work. Its legal, at least in the USA

I'm guessing that you are expected to work 8 hours a day for 5 days a week to obtain 40 hours total. But, if you were to work 40 hours in 4 days, then you should definitely get prior approval.

Did you have an arrangement/agreement with your employer before you took that 5th day off? If you didn't get prior approval, it will look like you worked 1 day less, even if you put in extra hours the other 4 days.

Furthermore, do you dock your hours somehow? How can you prove to your employer that you actually did work 40 hours that week? If you can't prove it, then how are they suppose to know? Like I said, next time, get prior approval before you do something like that.

I pretty much agree with I wish but want to clarify one point. Even if you prove you worked 40 hours in 4 days you still get docked. There is no 8 hour expectation X 5 days for a salaried person.

Agreed, first forget about 40 hour weeks, a salary person may have to work 50 to 60 or more hours a week, not just 40,
The company normally looks at if you take a full day off work, and will dock a "days" pay.

You would have had to get the companies approval prior to just taking off a day.