To evaluate the expression \( e^{-\frac{1}{900} \times 6} \), we first simplify the exponent:

\[
-\frac{1}{900} \times 6 = -\frac{6}{900} = -\frac{1}{150}
\]

Thus, the expression becomes:

\[
e^{-\frac{1}{150}}
\]

Now, using an approximation for \( e^{-\frac{1}{150}} \):

\[
e^{-\frac{1}{150}} \approx 0.99335
\]

So, the value of \( e^{-\frac{1}{150}} \) is approximately **0.99335**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. What is the general formula for the exponential function \( e^x \)?
2. How does the value of \( e^{-x} \) change as \( x \) increases?
3. Can you approximate \( e^{-1/150} \) using a series expansion of \( e^x \)?
4. What is the importance of the base \( e \) in calculus?
5. How do exponential functions behave in real-world applications like population growth or decay?

**Tip**: In calculus, exponential decay functions like \( e^{-x} \) are frequently used to model things that decrease over time, such as radioactive decay.

This problem involves simplifying and evaluating the exponential expression e^(-(1/900)*6), leading to an approximation of e^(-1/150) ≈ 0.99335. The solution highlights key concepts in exponential functions and algebra, suitable for students in Grades 10-12.

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