Question
Is 15 to the eighth power the same as saying (15 to the sixth power) to the second power?
Answers
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.
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.
Im confused, are you saying they are the same or not?
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!
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!