Summary: Use Windows PowerShell to display DHCP addresses in Windows 8.

 How can I use Windows PowerShell on my computer running Windows 8 to find IPV4 addresses
          that are supplied by DHCP?

 Use the Get-NetIPAddress function, and specify that the prefix origin is DHCP.
          You can also specify that the address is IPV4, and use other options to help identify what you seek,
          for example:

Get-NetIPAddress -AddressState preferred -AddressFamily ipv4 -Type unicast -PrefixOrigin dhcp