To simplify the expression \(\left(6^2\right)^4\), we can use the property of exponents known as the power of a power property. This property states that \((a^m)^n = a^{m \times n}\).
Given the expression \(\left(6^2\right)^4\):
1. Identify the base \(a\), the first exponent \(m\), and the second exponent \(n\):
- Base \(a = 6\)
- First exponent \(m = 2\)
- Second exponent \(n = 4\)
2. Using the power of a power property, multiply the exponents:
[tex]\[
6^{2 \times 4}
\][/tex]
3. Calculate the product of the exponents:
[tex]\[
2 \times 4 = 8
\][/tex]
So, the simplified expression is:
[tex]\[
6^8
\][/tex]
Therefore, the answer in the box should be [tex]\(6^{\boxed{8}}\)[/tex].
