1. **State the problem:** Calculate $25$ to the power of $2$ divided by $22.3452$. 2. **Write the expression:** The problem can be written as $$\frac{25^2}{22.3452}$$. 3. **Calculate the numerator:** $25^2 = 25 \times 25 = 625$. 4. **Substitute the numerator back:** $$\frac{625}{22.3452}$$. 5. **Perform the division:** $$\frac{625}{22.3452} \approx 27.96$$. 6. **Final answer:** The value of $\frac{25^2}{22.3452}$ is approximately $27.96$.