Your NEXUS card, along with related correspondence such as the conditional approval letter, will be mailed to the address you give. If you live in Alaska and are only in Washington temporarily, and expect to get your NEXUS card with your mail in Alaska, then use that address. If you expect to get the NEXUS card before you leave Washington, then you can use your Washington address.
You can change your mailing address at any time in the TTP system, so I would suggest you use your current address, and if you return to Alaska before your NEXUS interview, then change your address in the system.
Credit:stackoverflow.com‘