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

Question

?(1 point)
Responses

10,00015
10,000 superscript 15 baseline

10056
100 superscript 56 baseline

20015
200 superscript 15 baseline

100¹⁵

Answer 1

The Product Rule of Exponents states that when multiplying two expressions with the same base, you can add the exponents. In your case, you have:

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

Using the Product Rule:

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

Thus, the correct answer is:

\[ 100^{15} \]

So the correct response would be:

100¹⁵