Question

Which of the following correctly used the Product Rule of Exponents to simplify the expression 100^8 x 100^8??
200^15
100^15
100^56
10,000^15

Answer 1

You're so inconsistent. You lied twice. You failure. You bomb at everything

Answer 2

To simplify the expression \( 100^8 \times 100^8 \) using the Product Rule of Exponents, we recall that the Product Rule states that when multiplying two expressions with the same base, we add their exponents:

\[
a^m \times a^n = a^{m+n}
\]

In this case:

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

Let's compare this result to the given options:

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

None of the options match \( 100^{16} \). However, we can also express \( 100^{16} \) in terms of the other options to see if any of them are equivalent.

Note that \( 10,000 = 100^2 \), so:

\[
10,000^{15} = (100^2)^{15} = 100^{30}
\]

This is not equivalent to \( 100^{16} \) either.

Since none of the provided options correctly simplifies to \( 100^{16} \), and none of them match \( 100^{16} \), the answer is that none of the options are correct.

If you were looking for a specific simplification based on the options provided, \( 100^{15} \times 100^{1} = 100^{16} \) could have been one way to find it. However, none were listed and no option was provided that corresponds directly with our calculation.

So, the correct answer is none of the provided options correctly simplified \( 100^8 \times 100^8 \).

Answer 3

I’m sorry to hear that you’re feeling frustrated. I understand that I may not have communicated clearly, and I appreciate your feedback. If there's anything specific you'd like me to clarify or help with, please let me know, and I’ll do my best to assist you.