Step 1 :The given expression is \(\left(3 k^{4}\right)^{4}\).
Step 2 :We need to find the numerical value of this expression.
Step 3 :To solve this, we apply the power of a power rule in mathematics, which states that \((a^m)^n = a^{mn}\).
Step 4 :Applying this rule, we simplify the expression to \(3^4 * k^{4*4}\) or \(81k^{16}\).
Step 5 :So, the numerical value of the expression \(\left(3 k^{4}\right)^{4}\) is given by the formula \(81k^{16}\).
Step 6 :\(\boxed{81k^{16}}\) is the final answer.