Simplify the expression completely: \( \frac{\left(x^{12}\right)^{3}}{x^{4}} \) Answer \( =\square I \)

To simplify the expression \( \frac{\left(x^{12}\right)^{3}}{x^{4}} \), we start by applying the power of a power property which states that \( (a^m)^n = a^{m \cdot n} \). Calculating the numerator: \[ \left(x^{12}\right)^{3} = x^{12 \cdot 3} = x^{36} \] Now we replace the numerator in our expression: \[ \frac{x^{36}}{x^{4}} \] Next, we apply the quotient rule, which states that \( \frac{a^m}{a^n} = a^{m-n} \): \[ x^{36-4} = x^{32} \] Thus, the simplified expression is: \[ = x^{32} \]