Final answer:
The maximum number of unique IPv6 addresses is 2^128, which equals 340,282,366,920,938,463,463,374,607,431,768,211,456 possible addresses.
Step-by-step explanation:
The maximum number of unique IPv6 addresses possible is based on the length of the address, which is 128 bits. Since each bit has two possible values (0 or 1), the total number of unique addresses can be calculated using the formula 2^128. Put differently, this is 340,282,366,920,938,463,463,374,607,431,768,211,456 different addresses.