A multiple choice test has 10 items and each problem has four choices A, B, C, and D. How many different ways can the answer sheet be completed?

We will assume that all the questions are independent of each other, and that each question requires exactly one choice. That is the instruction "indicate all that apply" will not be applicable.

There are four ways to arrange the answers to the first question.
There are four ways to arrange the answers to the second question.
So there are 4*4=4²=16 ways to arrange the answer of the first two questions.

Continuing, there are four ways to arrange the answers of the third question, so there are 4*16=4³=64 ways to arrange the answers to the first three questions.

If you continue this way, how many ways can you arrange the answers to 10 questions?

To find the number of different ways to complete the answer sheet, we need to determine the number of choices for each problem and multiply them together.

Since each problem has four choices (A, B, C, and D), the number of choices for each problem is 4. Since there are 10 problems in total, we multiply the number of choices for each problem (4) by itself 10 times:

4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 = 4^10 = 1,048,576.

Therefore, there are 1,048,576 different ways to complete the answer sheet.