I need help with my math homework

Question

Your school is conducting a survey. Students can answer the questions in either part with “agree” or “disagree.”

a. What power of 2 represents the number of different ways that a student can answer all the questions in Part 1? _________

b. What power of 2 represents the number of different ways that a student can answer all the questions on the entire survey? ___________

c. The survey changes, and students can now answer “agree,” “disagree,” or “no opinion.” How does this affect your answers in parts (a) and (b)? They become_____  and______ , respectively.

Answer 1

2^13 for part one

2^23 for both parts

if 3 choices, then 3^13 and 3^23

convert the base from 3 to 2

3^13 =2^x

13ln3 = xln2

x =13ln3/ln2 = about 20.6

3^23 = 2^x

x = 23ln3/ln2 = about 36.5

3^13 = 2^20.6

3^23 = 2^35.5