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I’m not sure about Mint, but on Windows, the latest version of PowerPoint will allow you to save as MP4 instead of PPT format. PowerPoint will also allow you to imbed an MP4 in a PowerPoint presentation with the QuickTime plugin. Be aware that some of the 3rd party conversion programs have gotten poor reviews, so I would probably stay away from those. For example, Xilisoft’s converter has low scores from users on Cnet, so you might want to avoid that one.
All you need to do is open Office 2013, find the PPT or PPTX file that you want to convert to MP4 and open it. Then FILE>SAVE AS (pick a location). Then, choose MP4 from “save as type” option list and click SAVE.