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

Question

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.