1. The problem asks us to find the scale factor between two squares, where the left square has side length 9 and the right square has side length 40. 2. The scale factor is the ratio of a side length of the image (right square) to the corresponding side length of the original (left square). 3. Using the formula for scale factor: $$\text{Scale Factor} = \frac{\text{Side length of image}}{\text{Side length of original}}$$ 4. Substitute the given values: $$\text{Scale Factor} = \frac{40}{9}$$ 5. Since 40 and 9 have no common factors other than 1, the fraction is already in simplest form. 6. Therefore, the scale factor is: $$\boxed{\frac{40}{9}}$$