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, we use the rule that states \(a^m \times a^n = a^{m+n}\).

In this case:

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

Now, let's compare this to the options given:

1. \(200^{15}\)
2. \(100^{15}\)
3. \(100^{56}\)
4. \(10,000^{15}\)

None of these options is equivalent to \(100^{16}\). Therefore, it appears none of the provided options correctly represents the simplified form of \(100^8 \times 100^8\).