The expression you provided is:

$\exp\left(\frac{-36000^2}{600}\right)$

To calculate this, follow these steps:

Step 1: Square 36,000

$36000^2 = 1,296,000,000$

Step 2: Divide by 600

$\frac{1,296,000,000}{600} = 2,160,000$

Step 3: Apply the exponential function

Now, we calculate $\exp(-2,160,000)$. This is a very small number. The exponential function decays rapidly for large negative values, so:

$\exp(-2,160,000) \approx 0$

Result:

$\exp\left(\frac{-36000^2}{600}\right) \approx 0$

Since the number is so small, it's effectively zero for practical purposes.

Would you like to go deeper into how exponential decay works or explore something else? Here's a few follow-up questions:

1. How does the exponential function behave for very large negative values?
2. What would happen if the exponent were positive instead of negative?
3. Can you give an example where such an exponential decay is used in real-world scenarios?
4. What is the relationship between exponential decay and natural logarithms?
5. How do small values of exponential functions relate to probability in statistics?

Tip: When dealing with very large exponents, especially negative ones, the value of the exponential function quickly approaches zero.