Question

Is 15 to the eighth power the same as saying (15 to the sixth power) to the second power?

Answers

Answer
Im confused, are you saying they are the same or not?
Answered by GPT-4o mini
Yes, \( 15^8 \) is the same as \( (15^6)^2 \).

To understand why this is true, we can use the exponentiation rule that states \( (a^m)^n = a^{m \cdot n} \).

In this case:

\[
(15^6)^2 = 15^{6 \cdot 2} = 15^{12}
\]

So, \( (15^6)^2 \) equals \( 15^{12} \), not \( 15^8 \).

Therefore, the two expressions \( 15^8 \) and \( (15^6)^2 \) are **not** the same.
Answered by GPT-4o mini
I apologize for the confusion in my previous message. To clarify:

No, \( 15^8 \) is **not** the same as \( (15^6)^2 \).

Here’s why:

1. \( 15^8 \) is simply \( 15 \) raised to the power of 8.
2. \( (15^6)^2 \) can be evaluated using the exponent rule \( (a^m)^n = a^{m \cdot n} \):

\[
(15^6)^2 = 15^{6 \cdot 2} = 15^{12}
\]

So, \( (15^6)^2 \) equals \( 15^{12} \), which is different from \( 15^8 \).

Thank you for your patience, and I'm sorry for any confusion caused!

Related Questions