Question

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

Answer 1

Im confused, are you saying they are the same or not?

Answer 2

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.

Answer 3

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!