Is the windows 10 product key in BIOS?

Get into command prompt by searching for it or doing the Windows key and R button and typing cmd (it should pop up). Then type this command in exactly as is:

wmic path softwarelicensingservice get OA3xOriginalProductKey

And your product key should pop up right after. voila

sudo strings /sys/firmware/acpi/tables/MSDM | tail -1

Use this to view your product key from a live Ubuntu distro on pendrive

Microsoft has made it simple to activate Windows 10.

On new machines the product key is stored in BIOs and is used automatically by the Windows when connected to the Internet.

In Windows 10 hardware activation is used. Your Windows 10 will be automatically activated until you don't make changes to the hardware.

If you want to install same version as fresh no problem click I don't have a product key link during installation and it will be activated automatically.

You can also switch between 32-bit and 64-bit without need of a key in the same edition.

If you want to see OEM details visit Microsoft live and check devices tab. You will get everything there.