A router learned 10.0.0.0/8, 10.0.0.0/16, and 10.0.0.0/24. Which show ip route output correctly displays all three prefixes?

The correct output displays all three distinct prefixes (10.0.0.0/8, 10.0.0.0/16, and 10.0.0.0/24) because a router can maintain multiple entries for the same major network if they have different subnet masks. This is known as route specificity; the router will always prefer the most specific (longest prefix match) route when forwarding traffic. The other options are incorrect because they only show one or two of the learned prefixes, not all three. A router's routing table will list all learned routes unless they are superseded by a more specific route to the exact same destination, which is not the case here as the subnet masks differ.