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

Question

Responses

10,00015
10,000 superscript 15 baseline

20015
200 superscript 15 baseline

10015
100 superscript 15 baseline

10056

Answer 1

To simplify the expression \( 1008 \cdot 1007 \) using the Product Rule of Exponents, we first express \( 1008 \) and \( 1007 \) in terms of their base \( 100 \):

1. \( 1008 = 100^{8} \)
2. \( 1007 = 100^{7} \)

Now using the Product Rule of Exponents, which states that when you multiply like bases you add the exponents:

\[ 100^{8} \cdot 100^{7} = 100^{8+7} = 100^{15} \]

Thus, the correct answer is:

10015 (100 superscript 15 baseline).