1. **State the problem:** Simplify the expression $$\sqrt[3]{\frac{18}{125}}$$. 2. **Recall the cube root property:** The cube root of a fraction is the fraction of the cube roots, i.e., $$\sqrt[3]{\frac{a}{b}} = \frac{\sqrt[3]{a}}{\sqrt[3]{b}}$$. 3. **Apply the property:** $$\sqrt[3]{\frac{18}{125}} = \frac{\sqrt[3]{18}}{\sqrt[3]{125}}$$ 4. **Simplify the denominator:** Since $$125 = 5^3$$, we have $$\sqrt[3]{125} = 5$$ 5. **Simplify the numerator:** Factor 18 as $$18 = 9 \times 2 = 3^2 \times 2$$. Since 3 is not a perfect cube, we keep it inside the root: $$\sqrt[3]{18} = \sqrt[3]{3^2 \times 2} = \sqrt[3]{3^2} \times \sqrt[3]{2}$$ 6. **Write the simplified expression:** $$\frac{\sqrt[3]{18}}{\sqrt[3]{125}} = \frac{\sqrt[3]{3^2 \times 2}}{5} = \frac{\sqrt[3]{18}}{5}$$ 7. **Final answer:** $$\boxed{\frac{\sqrt[3]{18}}{5}}$$ This is the simplest exact form since 18 is not a perfect cube and cannot be simplified further under the cube root.