Final answer:
There are 439,804,651,110,400 different ways a student can complete a multiple-choice test consisting of 21 questions with four possible answers.
Step-by-step explanation:
The possible ways to complete a multiple-choice test consisting of 21 questions, with each question having four possible answers (a, b, c, or d), can be calculated using the concept of permutations.
The total number of ways to choose one answer for each question is 4 raised to the power of 21, because each question has 4 options.
So, the total possible ways to complete the test is 4²¹ = 439,804,651,110,400.
This means that there are 439,804,651,110,400 different ways a student can complete the multiple-choice test.