First rule of using a video frame for an image source: Pixels is pixels.
If you have an 8k video image, you have 7680 × 4320 pixels. Period. No more, no less.
Export your video frame in a lossless format like tiff or bmp and you get all 33 megapixels in their original glory.
DPI has no meaning in a digital image until you want to print or display it.
Once you decide you want to print it, you need to do some math. How big do you want the print to be? What aspect ratio/orientation do you want?
The original frame is in a 16:9 format. If you want an 8x10 print, you will have to crop the image to make a portion of that 16:9 frame fit in an 8x10 frame. Should the 8x10 be landscape or portrait orientation?
If we assume that you keep all the pixels of your source image in the vertical dimension, your 8x10 cropped image will have pixel dimensions of 3456 wide (the "8" part) x 4320 high (the "10" part).
If we further assume that a dpi of 300 pixels/inch gives the razor-sharp print resolution that you want, then your 8x10 print from an 8k image source can be as big as 11.5 inches x 14.4 inches. An 8x10 image from that video frame printed at 150 dpi (often acceptable and visibly sharp) can be double that: about 23 inches by 29 inches.
This is just one example. But you should always remember the rule when saving a video frame as a digital image: pixels is pixels.