Simplify the given expression below. Leave the answer in exponential notation. \( (6 w)^{2} \cdot\left[(6 \mathrm{w})^{8}\right]^{4} \) \( (6 \mathrm{w})^{2} \cdot\left[(6 \mathrm{w})^{8}\right]^{4}=\square \) (Simplify your answer. Type your answer using exponential notation. Do not perform the calculation.)

To simplify the expression, we first apply the power of a power rule. We start with \( (6w)^2 \cdot \left[(6w)^8\right]^4 \). Using the rule \((a^m)^n = a^{m \cdot n}\), we transform the second term: \[ (6w)^2 \cdot (6w)^{8 \cdot 4} = (6w)^2 \cdot (6w)^{32} \] Next, we apply the product of powers rule \(a^m \cdot a^n = a^{m+n}\): \[ (6w)^{2 + 32} = (6w)^{34} \] Thus, the simplified expression is: \[ (6w)^{34} \]