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

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

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

When we multiply these two exponential terms, we can use the Product Rule of Exponents, which states that \(a^m \cdot a^n = a^{m+n}\). Therefore,

\[ 1008 \cdot 1007 = 10^{8} \cdot 10^{7} = 10^{8+7} = 10^{15} \]

Since \(100 = 10^2\), we also express the result as:

\[ 10^{15} = (10^2)^{15/2} = 100^{15} \]

Thus, the expression simplifies to \(100^{15}\).

Looking at the options provided:

1. \(100^{56}\)
2. \(100^{15}\) (This is correct)
3. \(10,000^{15}\) (This is equivalent to \(100^{30}\))
4. \(200^{15}\)

The correct response using the Product Rule of Exponents is:

100^{15}