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

?(1 point)
Responses

10056
100 superscript 56 baseline

10,00015
10,000 superscript 15 baseline

10015
100 superscript 15 baseline

20015

1 answer

To simplify the expression \( 1008 \cdot 1007 \) using the Product Rule of Exponents, we start by rewriting \( 1008 \) and \( 1007 \) in terms of powers of 10:

\[ 1008 = 10^8 \quad \text{and} \quad 1007 = 10^7 \]

Now, we can apply the Product Rule of Exponents, which states that \( a^m \cdot a^n = a^{m+n} \):

\[ 10^8 \cdot 10^7 = 10^{8+7} = 10^{15} \]

So, the correct simplification of the expression \( 1008 \cdot 1007 \) is \( 100^{15} \).

Among the provided options, the one that represents this simplification correctly is:

10015 100 superscript 15 baseline.