If you like, here's more details about exFAT below.
When you right click on a drive and click on Format, the exFAT option is only available for removable drives like a USB flash drive.
However, you should be able to format the internal hard drive as exFAT in the command prompt using the command below as a workaround. Substitute F for your drive letter instead.
Format F: /A:64K /FS:ExFAT