Question 269139
For each question there are 4 ways to select a wrong answer. Using the rule that says if event A occurs in m ways and event B occurs in n ways then A and B can occur together in m*n ways we know that wrongly answering question 1 occurs in 4 ways. For each to these ways there are 4 ways to wrongly answer question 2 and so on for questions 3 through 10. So for the number of ways to wrongly answer ten times we have:

4*4*4*4*4*4*4*4*4*4 = 4^10