1. **State the problem:** Find an expression equivalent to $\left(2x\right)^{-3}$. 2. **Recall the negative exponent rule:** For any nonzero number $a$, $a^{-n} = \frac{1}{a^n}$. 3. **Apply the rule:** $$\left(2x\right)^{-3} = \frac{1}{\left(2x\right)^3}$$ 4. **Evaluate the cube:** $$\left(2x\right)^3 = 2^3 \cdot x^3 = 8x^3$$ 5. **Substitute back:** $$\frac{1}{\left(2x\right)^3} = \frac{1}{8x^3}$$ 6. **Final answer:** The expression equivalent to $\left(2x\right)^{-3}$ is $\frac{1}{8x^3}$. --- **Note:** The correct choice is D) $\frac{1}{8x^3}$.