To calculate $(252^2) \cdot (210^2)$, we can proceed as follows:

Step 1: Use the identity $(a^2)(b^2) = (ab)^2$

$(252^2) \cdot (210^2) = (252 \cdot 210)^2$

Step 2: Multiply $252$ and $210$

$252 \cdot 210 = 52920$

Step 3: Square the result

$52920^2 = 2,799,806,400$

Final Answer:

$(252^2) \cdot (210^2) = 2,799,806,400$

Would you like a detailed breakdown or have additional questions?

Related Questions:

1. How is the identity $(a^2)(b^2) = (ab)^2$ derived?
2. What is the prime factorization of 52920?
3. How can we compute such large squares more efficiently?
4. Can you explain the rules of exponents in this context?
5. How does this calculation relate to geometry or physics?

Tip: For very large calculations, using logarithmic properties can simplify the process significantly.