Final answer:
There are a total of 36 possible outcomes for each roll of two identical six-sided dice, and when rolled 10 successive times, the sequences of outcomes are found by raising 36 to the power of 10, which is 36^10.
Step-by-step explanation:
The question on how many sequences of outcomes are possible when rolling two identical dice 10 successive times falls under the category of combinatorics, a branch of mathematics. For any given single roll of two identical six-sided dice, there are a total of 36 possible outcomes (6 sides on the first die multiplied by 6 sides on the second die). Since the dice are identical, the order does not matter, E.g., rolling a 3 and a 5 is the same as rolling a 5 and a 3. Therefore, we need to account for the combinations without repetitions, which in this case remains 36 since each combination is unique (1,1; 1,2; ... ; 6,6).
When rolling these two dice 10 successive times, each roll is independent, and the total number of sequences of outcomes equals the number of single-roll outcomes raised to the power of the number of rolls. Therefore, we calculate the total number of sequences by raising the number of outcomes of one roll to the power of 10: 3610.