$\left(-27 x^{12}\right)^{\frac{1}{3}}$
Final Answer: $\boxed{-3x^4}$
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: $\boxed{-3x^4}$