CHALLENGE

Your school is conducting a poll that has two parts. The first part has 13 questions, and the second part has 10 questions. Students can answer each question with "agree" or "disagree."

1. What power of 2 represents the number of ways to answer the questions in the first part of the poll?
2. What power of 2 represents the number of ways to answer the questions in the second part of the poll?
3. What power of 2 represents the number of ways to answer all of the questions on the poll?

The number of ways to answer the poll questions in each part is determined by the power of 2 representing the choices. The total number of ways to answer all questions is the product of the ways to answer each part.

Explanation:

The number of ways to answer the questions in the first part of the poll:

For each of the 13 questions, students can choose either 'agree' or 'disagree,' which gives 2 choices for each question. Therefore, the total number of ways is 2^13.

The number of ways to answer the questions in the second part of the poll:

Similarly, for the 10 questions in the second part, there are 2 choices for each question, resulting in 2^10 ways to answer.

The number of ways to answer all questions on the poll:

Since the two parts are independent, the total number of ways to answer all questions is the product of the ways to answer each part: 2^13 x 2^10 = 2^23.

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