Question

Which factors of the base would help simplify the expression 16 ? (1 point)
16 = 8 • 8
• 16 = 2 • 2•2•2
• 16 = 4•2•2
• 16 = 4•4

Answer 1

To simplify the expression for 16, we can express it in different ways based on its prime factorization:

1. **16 = 8 • 8**
- This breaks 16 down into two factors of 8, but 8 can itself be simplified further since 8 = 2 • 2 • 2.

2. **16 = 2 • 2 • 2 • 2**
- This expression shows the prime factorization of 16, which is simple and clear as it uses the base factor of 2.

3. **16 = 4 • 2 • 2**
- This can be simplified further since 4 = 2 • 2. Thus, it can also be represented as 16 = (2•2) • 2 • 2.

4. **16 = 4 • 4**
- This expression shows that 16 can be simplified as two factors of 4, where 4 can further be expressed as 2 • 2.

For simplification, the factorization into prime factors (2) is often the most useful, indicating that 16 is \(2^4\).

Overall, all the given expressions are technically equal to 16, but using \(2^4\) or representing it as \(2 • 2 • 2 • 2\) provides a direct way to simplify and shows its base factor clearly.

The **most simplified representation** in terms of prime factorization is:
- **16 = 2 • 2 • 2 • 2 or 16 = 2^4**.

Thus, for simplifying based on the base factors, the expression **16 = 2 • 2 • 2 • 2** directly shows its prime factorization and reflects the use of the base factor effectively.