To determine how many different ways a true-false test consisting of 9 questions can be answered, we can approach this by recognizing that each question has 2 possible answers: true or false.
For each of the 9 questions, since there are 2 independent choices (true or false), we can calculate the total number of ways to answer the test using the formula for combinations of independent events. Specifically, this can be expressed as:
Number of ways = 2^n
Where n is the number of questions. In this case, n is 9. Thus, we have:
Number of ways = 2^9 = 512
This means that there are a total of 512 different combinations of answers possible for a test with 9 true-false questions. Each combination represents a unique set of answers ranging from all questions answered as true to all answered as false, and every variation in between.