To find the value of the given expression, follow these steps:

1. Calculate the squares: $5^2 = 25 \quad \text{and} \quad 2^2 = 4$

2. Substitute these values back into the expression: $\frac{3}{5^2} \times \frac{1}{2^2} = \frac{3}{25} \times \frac{1}{4}$

3. Multiply the fractions: $\frac{3}{25} \times \frac{1}{4} = \frac{3 \times 1}{25 \times 4} = \frac{3}{100}$

Therefore, the value of the expression is $\frac{3}{100}$.

Would you like more details or have any questions?

Here are 5 questions you might want to ask:

1. How do you multiply fractions?
2. What are the steps to simplify fractions?
3. Can you explain how to square a fraction?
4. How do you add and subtract fractions?
5. What is the difference between multiplying and dividing fractions?

Tip: When multiplying fractions, multiply the numerators together and the denominators together to get the result.