1. **State the problem:** We have two squares, one with side length 18 units and the other with side length 66 units. We need to find the scale factor from the smaller square to the larger square. 2. **Formula:** The scale factor between two similar figures is the ratio of corresponding side lengths. Here, it is $ \frac{\text{side length of larger square}}{\text{side length of smaller square}} $. 3. **Calculate the scale factor:** $$\text{Scale factor} = \frac{66}{18}$$ 4. **Simplify the fraction:** $$\frac{66}{18} = \frac{\cancel{6} \times 11}{\cancel{6} \times 3}$$ $$= \frac{11}{3}$$ 5. **Interpretation:** The scale factor from the smaller square to the larger square is $ \frac{11}{3} $. This means each side of the larger square is $ \frac{11}{3} $ times the length of the smaller square's side. **Final answer:** The scale factor is $ \frac{11}{3} $.