Of course, it takes only 1 hour and 10 minutes from Roma Termini Station to Napoli Centrale Station.
https://www.lefrecce.it/B2CWeb/search.do?parameter=searchOutputViewer&cFID=yccLrRJxTJ16
Prices are not fixed, there's promotions (look for the Base Economy fare), even more when you book at the beginning of each month (going as far as paying only 10 for the fastest train Rome to Milano -and viceversa- which is usually >80) and you usually pay way less if you book in advance, especially if >1 week.
Then you take a train from Napoli Centrale to Pompeii using the Circumvesuviana train route, there's a train every 30min and it takes roughly 40minutes to get there, costs 4.
To get back in Rome, the last (high-speed) train from Napoli Centrale is around 7:30 PM and gets you to Stazione Termini by 8:40PM.
All in all, if you find no promotions at all and book at the very last minute, you're going to spend 90 for the whole trip using the Freccia (arrow) train (high-speed train) for Rome>Napoli and back and using the cheapo county train for Napoli>Pompeii and back.
*DON'T LOOK/BOOK a train to get straight to Pompeii leaving from Rome* it's slower and more expensive with a terrible timetable to boot.