Final answer:
The total number of different equally likely outcomes when a six-sided die is rolled six times is 46,656, calculated as 6 raised to the 6th power.
Step-by-step explanation:
When you roll a fair six-sided die, there are 6 possible outcomes for each roll. If you roll the die 6 times, each roll is independent of the others. To find the total number of different equally likely outcomes, you multiply the number of outcomes for each roll by itself for each successive roll.
This is because for each outcome of the first roll, there are 6 possible outcomes for the second roll, and so on.
The calculation for the total number of outcomes is 6 × 6 × 6 × 6 × 6 × 6, which can be written as 6^6. Therefore, the total number of different possible outcomes when a six-sided die is rolled six times is 46,656.