$\left(-27 x^{12}\right)^{\frac{1}{3}}$

Step 1 ：Given expression: $\left(-27 x^{12}\right)^{\frac{1}{3}}$

Step 2 ：Using the property $(a^m)^n = a^{mn}$, we get: $(-27)^{\frac{1}{3}}(x^{12})^{\frac{1}{3}}$

Step 3 ：Calculating the cube root of -27: $\sqrt[3]{-27} = -3$

Step 4 ：Simplifying the exponent: $(x^{12})^{\frac{1}{3}} = x^{12 \times \frac{1}{3}} = x^4$

Step 5 ：Final Answer: $\boxed{-3x^4}$