The Product Rule of Exponents states that when you multiply two powers with the same base, you add the exponents.
In this case, the expression can be interpreted as:
\[ 100 \times 100 = 100^{1} \times 100^{1} = 100^{1+1} = 100^{2} \]
Now, \( 100^{2} = 10,000 \).
Thus, the correct simplification of \( 100 \times 100 \) according to the Product Rule of Exponents is:
10,000.