Question

Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007
?(1 point)
Responses

200^15
200 superscript 15 baseline

100^15
100 superscript 15 baseline

100^56
100 superscript 56 baseline

10,000^15

Answer 1

To simplify the expression \( 1008 \cdot 1007 \) using the Product Rule of Exponents, we first rewrite both 1008 and 1007 in terms of base 10.

1. \( 1000 = 10^3 \)
2. \( 100 = 10^2 \)

However, we notice that neither 1008 nor 1007 is an exact power of 10. They can be rewritten more generally but would depend on how we want to express it.

Instead, let's rewrite 1008 and 1007 directly:
- \( 1000 + 8 = 10^3 + 8 \)
- \( 1000 + 7 = 10^3 + 7 \)

Yet, if we want to proceed with expressions using powers of 10:

- \( 100 = 10^2 \)
- \( 10,000 = 10^4 \)

A more straightforward method would be:
- \( 1008 = 10^3 + 8 \)
- \( 1007 = 10^3 + 7 \)

The key idea is that individually simplifying \( 1008 \cdot 1007 \) into a form resembling a power of ten boils down to finding the product properly.

Since the options provided are more about powers, the correct choice here depends on identifying the powers fitting of such multiplication.

Thus, only one option resembles a notable expression of the calculation:
- \( 100^15 \) makes sense properly as an exponentiation.

Therefore, the most appropriate use in context given standard simplification forms would be:

**Correct Option: \( 100^{15} \)**

Thus, the answer is:

**100^15**.