Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007

Question

?(1 point)
Responses

20015
200 superscript 15 baseline

10,00015
10,000 superscript 15 baseline

10015
100 superscript 15 baseline

10056
100 superscript 56 baseline
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Answer 1

To simplify the expression \(1008 \cdot 1007\) using the Product Rule of Exponents, we recognize that when multiplying like bases, we add the exponents.

In this case:

\[ 1008 \cdot 1007 = 100^{8} \cdot 100^{7} \]

Using the Product Rule, we add the exponents:

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

So, the correct simplified expression is:

10015 (or \(100^{15}\)).