Question

16 of 2016 of 20 Items

















Question
Which of the following is equivalent to the expression?

3632


(1 point)
Responses

34
3 to the 4th power

38
3 to the 8th power

33
3 cubed

312

Answer 1

To find which of the following is equivalent to the expression \( 3632 \), we should first try to express \( 3632 \) in terms of powers of \( 3 \).

Calculating \( 3^4 \), \( 3^8 \), \( 3^3 \), and \( 3^{12} \):

1. \( 3^3 = 27 \)
2. \( 3^4 = 81 \)
3. \( 3^8 = 6561 \)
4. \( 3^{12} = 531441 \)

Now, let's analyze the responses against \( 3632 \):

- \( 3^4 = 81 \)
- \( 3^8 = 6561 \)
- \( 3^3 = 27 \)
- \( 3^{12} = 531441 \)

Clearly, none of these match \( 3632 \). So let's consider if we should convert \( 3632 \) into a product of components representing \( 3 \).

Let's check the prime factorization of \( 3632 \):

- Dividing by \( 2 \):
- \( 3632 \div 2 = 1816 \)
- \( 1816 \div 2 = 908 \)
- \( 908 \div 2 = 454 \)
- \( 454 \div 2 = 227 \) (227 is a prime number)

Thus, \( 3632 = 2^4 \times 227 \).

Since none of the options are a breakdown of \( 3632 \) and if we only consider the options given, none of them are equivalent to \( 3632 \).

If this is a multiple-choice question, please review the available choices, as none are completed equivalent at face value from the calculations. If the question has additional context or instructions, that may influence what type of conversion or interpretation is expected.