1. **State the problem:** Simplify the expression $$\frac{(2xr)^0}{x - 2y^3 - 2xr^3}$$. 2. **Recall the rule:** Any nonzero number or expression raised to the power 0 equals 1, i.e., $$a^0 = 1$$ for $$a \neq 0$$. 3. **Apply the rule to the numerator:** Since $$(2xr)^0 = 1$$ (assuming $$2xr \neq 0$$), the expression becomes: $$\frac{1}{x - 2y^3 - 2xr^3}$$ 4. **Final simplified form:** The expression simplifies to: $$\boxed{\frac{1}{x - 2y^3 - 2xr^3}}$$ This is the simplest form unless further factorization of the denominator is possible, which is not requested here.