Final answer:
There are 256 different possible outcomes when rolling four distinct, four-sided dice, calculated by raising the number of outcomes for one die (4) to the power of the number of dice (4) rolled.
Step-by-step explanation:
The question asks how many different outcomes are possible when four distinct, four-sided dice are rolled. Since each die is four-sided, and each side can show a number between 1 and 4, each die has 4 possible outcomes. When considering multiple dice, we determine the number of total outcomes by multiplying the number of outcomes for a single die by itself for each additional die.
Therefore, we calculate the total number of different outcomes by raising the number of outcomes for one die to the power of the number of dice rolled:
Number of outcomes = 44 = 256
Hence, there are 256 different possible outcomes when rolling four distinct, four-sided dice.