Final answer:
In a binary tree with 296 nodes, the maximum number of leaf nodes can be 296, as a binary tree of height 9 could potentially have up to 512 leaves, and we have only 296 nodes in total.
Step-by-step explanation:
In a binary tree, each node can have at most two children, and nodes with no children are called leaves. The binary tree with 296 nodes would have a maximum number of leaves when it is a complete binary tree except for the last level, which might not be completely filled. In this ideal case, the bottom level of the tree would have as many leaves as possible, while all other nodes would have two children each.
To find the maximum number of leaf nodes, we use the property that in a complete binary tree of height h, the maximum number of leaf nodes is 2h-1. Now, a binary tree with 296 nodes must have a height of at least 9 (since 28 = 256 is less than 296, and 29 = 512 is more than 296). However, because not all nodes on the last level would be filled, we know the height of the tree is 9 with some leaves missing from the potentially 512 at the bottom level.
The tree could have a maximum of 296 - (2h-1 - 1), which would be the number of internal nodes with two children each, therefore, the number of leaf nodes would be 512 - (512 - 296) = 296. So, in a binary tree with 296 nodes, the maximum number of leaf nodes can be 296.