Simplify the expression completely: \( \left(\frac{z^{4}}{3}\right)^{3} \) Use no parentheses in your answer. Answer \( =\square I \)

To simplify the expression \( \left(\frac{z^{4}}{3}\right)^{3} \), we will apply the power of a quotient rule as well as the power of a power rule. First, calculate the numerator: \[ (z^{4})^{3} = z^{4 \cdot 3} = z^{12} \] Now, calculate the denominator: \[ (3)^{3} = 3^{3} = 27 \] Putting it all together, we get: \[ \frac{z^{12}}{27} \] So the final answer is: \[ = \frac{z^{12}}{27} I \]