SOLUTION: Assume that the test has 15 questions, each with 6 choices for the answer. An answer sheet has one answer for each question. How many different answer sheets are possible

Assume that the test has 15 questions, each with 6 choices for the
answer.  An answer sheet has one answer for each question.

We can choose the correct answer for the 1st question any of 6 ways.
So that's 6 ways to choose the correct answer for the first question.

For each of the 6 ways we can choose the correct answer for the 1st question,
we can choose the correct answer to the 2nd question any of 6 ways. 
So that's 6·6 or 36 ways to choose the correct answers for the first 2
questions.

For each of the 6·6 or 6² or 36 ways we choose the correct answer for the 
1st 2 questions, we can choose the correct answer to the 3rd question any of 6
ways. So that's 6·6·6 or 6³ or 216 ways to choose the correct answer for the
first 3 questions.

For each of the 6·6·6 or 6³ or 216 ways we choose the correct answer for the
1st 3 questions, we can choose the correct answer to the 4th question any of 6
ways. So that's 6·6·6·6 or 6⁴or 1296 ways to choose the correct answer for the
first 4 questions.

etc., etc., and finally,

For each of the 6·6·6·6·6·6·6·6·6·6·6·6·6·6 or 614 ways we choose the correct 
answer for the 1st 14 questions, we can choose the correct answer to the 15th
question any of 6 ways. So that's 6·6·6·6·6·6·6·6·6·6·6·6·6·6·6 or 615 ways to 
choose the correct answer for the first 15 questions, which is all of them.

Answer 615 = 470184984576 ways.

Edwin