1. The problem asks for the square of the fraction \(\frac{25}{9}\). 2. To square a fraction, we square both the numerator and the denominator separately. 3. Square the numerator: \(25^2 = 625\). 4. Square the denominator: \(9^2 = 81\). 5. Therefore, \(\left(\frac{25}{9}\right)^2 = \frac{625}{81}\). 6. The fraction \(\frac{625}{81}\) is already in simplest form. Final answer: \(\frac{625}{81}\).