Chapter 11 - Counting Methods and Probability Theory - 11.1 The Fundamental Counting Principle - Exercise Set 11.1 - Page 693: 16

$6561$

The number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur. --------- The number of ways to choose the answer to the ... 1st question is 3, 2nd question is 3, 3rd question is 3, ... 7th question is 3, 8th question is 3. By the Fundamental Counting Principle, the total ways of doing this is $3\times 3\times...\times 3=3^{8}=6561$ ways