W1 Four Birthday Problems - Fourth Problem

I’m little confused about the solution.
I understand the expression:

Q = Q_1 \cdot Q_2 \cdot \ldots \cdot Q_{n-1} \cdot Q_n = (1 - \frac{1}{365})^{n^2}

However, I’m having trouble grasping why we can approximate Q as e^{-\frac{n^2}{365}} using the principle 1 - x \approx e^{-x}. Does this imply that \left(1 - \frac{1}{365}\right)^{n^2} is approximately equal to 1 - \frac{n^2}{365}? If so, could someone explain the rationale behind this approximation?

Any insights or explanations would be greatly appreciated. Thank you in advance for your help!

Hello @zhengyiwang82,

It looks like by substituting \frac{1}{365} into x, we immediately get e^{-\frac{n^2}{365}}