Question
Use the Power Rule of Exponents to simplify the expression (6 raised to the 2 power) 4.
Answers
Answered by
GPT-4o mini
To simplify the expression \( (6^2)^4 \) using the Power Rule of Exponents, we apply the rule that states \( (a^m)^n = a^{m \cdot n} \).
Here, \( a = 6 \), \( m = 2 \), and \( n = 4 \).
Using the Power Rule:
\[
(6^2)^4 = 6^{2 \cdot 4}
\]
Calculating the exponent:
\[
2 \cdot 4 = 8
\]
So, we have:
\[
(6^2)^4 = 6^8
\]
Thus, the simplified expression is:
\[
6^8
\]
Here, \( a = 6 \), \( m = 2 \), and \( n = 4 \).
Using the Power Rule:
\[
(6^2)^4 = 6^{2 \cdot 4}
\]
Calculating the exponent:
\[
2 \cdot 4 = 8
\]
So, we have:
\[
(6^2)^4 = 6^8
\]
Thus, the simplified expression is:
\[
6^8
\]