Question

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

20015
200 superscript 15 baseline

10056
100 superscript 56 baseline

10,00015
10,000 superscript 15 baseline

10015

Answer 1

To simplify the expression \( 1008 \cdot 1007 \) using the Product Rule of Exponents, we can rewrite the bases with an exponent.

The expression leverages the property:
\[
a^m \cdot a^n = a^{m + n}
\]

Here, we have:
\[
1008 = 100^8 \quad \text{and} \quad 1007 = 100^7
\]

So, the expression becomes:
\[
100^8 \cdot 100^7 = 100^{8 + 7} = 100^{15}
\]

Thus, the correctly simplified expression is:
\[
100^{15}
\]

Therefore, the correct answer is:
**10015**.