To simplify the expression \((6^2)^4\) using the power rule of exponents, you can apply the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\).
Here’s how to apply it to the given expression:
\[ (6^2)^4 = 6^{2 \cdot 4} = 6^8 \]
Now, if you want to get the numerical value of \(6^8\):
Calculating \(6^8\):
\[ 6^8 = 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 = 1,679,616 \]
Thus, the simplified expression is:
\[ 6^8 \quad \text{or} \quad 1,679,616 \]
So the final answers are:
- Simplified expression: \(6^8\)
- Numerical value: \(1,679,616\)