To solve the problem, we need to evaluate the given expression [tex]\(\left(6^2\right)^7\)[/tex] and compare it with the powers of 6 listed in the options.
Start with the given expression:
[tex]\[
\left(6^2\right)^7
\][/tex]
First, let's simplify the exponentiation using the power rule [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]:
[tex]\[
\left(6^2\right)^7 = 6^{2 \cdot 7}
\][/tex]
Calculate the exponent:
[tex]\[
2 \cdot 7 = 14
\][/tex]
So, the simplified form of [tex]\(\left(6^2\right)^7\)[/tex] is:
[tex]\[
6^{14}
\][/tex]
Thus, the correct expression that matches [tex]\(\left(6^2\right)^7\)[/tex] from the given options is:
[tex]\[
6^{14}
\][/tex]
The numerical value of [tex]\(6^{14}\)[/tex] can be calculated as:
[tex]\[
6^{14} = 78,364,164,096
\][/tex]
Therefore, the correct and simplified form of the given expression [tex]\(\left(6^2\right)^7\)[/tex] is [tex]\(6^{14}\)[/tex].
