Answer:
512 branches.
Explanation:
We are asked to find the number of branches a tree diagram that represents total number of ways to flip 9 coins.
We know that when we flip a coin, we get two outcomes: heads or tails.
When we will flip 9 coins, the number of outcomes would be 2 multiplied to itself by 9 times that would be:

Therefore, the tree diagram that representing the total number of ways to flip 9 coins would have 512 branches.