Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Yes, the first link is for the base "2007 compatibility Pack". If you can open the 4 letter extensions then yes it is installed. Good for you.
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The second link is for the most recent update to the compatibility pack. Since you already had the compatibility pack, Office update has probably already applied the SP3 update. If you want to double check, down load and run it. If it says you already have it, again great.
Yes, the old 3 letter file types are DOC, XLS, PPT
New 4 letter "x-file" types are DOCX, XLSX, PPTX, and DOCM, XLSM, PPTM for macro enabled files
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If you are still using any files with the old 3 letter file types it is strongly recommended to convert them to the new 4 letter file types. Most of your files should be the non-macro "X" types.
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The point of the new file types is to only allow macros to be saved in the few files you need to contain them. Most of your files should be the X, non macro, type.
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Happy computing.