Start with the physical size on the slide in inches. Lets say it's 5 x 6
If you compress to 220 dpi (assuming it was more than this to start with) it will be 1100px x 1320px (ie 5 x 220 and 6 x220). The original dpi is not relevant as long as it's more than the target.
I would never use PPT to resize jpgs because as well as resizing with little flexibility it can also increase the jpg compression and reduce quality.
A good free tool is Irfanview
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