a) To determine the prefix to use, we need to calculate the number of bits needed to support the maximum number of networks and the minimum number of hosts per network. The minimum number of hosts per network is 500, which requires at least 9 bits (since 2^9 = 512). To support the maximum number of networks, we need to find the highest power of 2 that is less than or equal to the number of networks. In this case, 2^11 = 2048, so we need 11 bits for the network portion of the address. Therefore, the prefix to use is /27, since we're using 16 bits for the network portion of the address and 11 bits for the host portion (16 + 11 = 27).
b) The subnet mask to use for a /27 prefix is 255.255.255.224. This is because a /27 prefix uses the first 27 bits of the 32-bit address for the network portion, which leaves 5 bits for the host portion. Converting these 5 bits to decimal gives us 2^5 = 32, so each subnet has 32 addresses. Subtracting 2 from this (one address for the network and one address for the broadcast) gives us 30 usable addresses per subnet.
c) Using a /27 prefix, we can create up to 2048 (2^11) networks, each with up to 30 usable addresses. The first four networks would be:
Network Address Subnet Mask Usable Address Range Broadcast Address
80.0.0.0 255.255.255.224 80.0.0.1 - 80.0.0.30 80.0.0.31
80.0.0.32 255.255.255.224 80.0.0.33 - 80.0.0.62 80.0.0.63
80.0.0.64 255.255.255.224 80.0.0.65 - 80.0.0.94 80.0.0.95
80.0.0.96 255.255.255.224 80.0.0.97 - 80.0.0.126 80.0.0.127
Note that the network address and broadcast address are not usable for hosts, which is why we subtract 2 from the total number of addresses per subnet to get the number of usable addresses.