Which of the following correctly used the Product Rule of Exponents to simplify the expression 100^8 x 100^8?

Question

200^15
100^15
100^56
10,000^15

Answer 1

To simplify the expression \(100^8 \times 100^8\) using the Product Rule of Exponents, which states that \(a^m \times a^n = a^{m+n}\):

\[ 100^8 \times 100^8 = 100^{8+8} = 100^{16} \]

Now, let’s analyze the options provided:

1. \(200^{15}\) – This does not match.
2. \(100^{15}\) – This does not match.
3. \(100^{56}\) – This does not match.
4. \(10,000^{15}\) – This is \( (100^2)^{15} = 100^{30} \) (not a match).

None of the given options accurately represents the simplified expression \(100^{16}\).

However, if we are asked about equivalent expressions that can be derived through other means (with possible exponents), none match \(100^{16}\) directly. The best we can say is that the correct answer, \(100^{16}\), is not among the options listed.