Every device connected to a network requires an IP address. Without an IP address, other devices cannot communicate with the device although the device may be physically connected. The same goes for wireless access points and routers such as the AirPort Extreme. If you are able to access the device or even use the device to connect to the Internet, then the device has an IP address. As long as you are connected to the AirPort Extreme, you can find its IP.
Connect to the AirPort Extreme using a Wi-Fi enabled device.
Launch a command prompt or terminal window. On Microsoft Windows, type "cmd" into the Search field of the Start menu and click the "Command Prompt" option. Under GNU/Linux or Mac OS X, launch a terminal window from the Applications folder.
Type "ipconfig" for Microsoft Windows or "route" for GNU/Linux or Mac OS X. The IP address listed under Gateway is the AirPort Extreme's IP address.