Calculating \( 3^{274} \) directly results in an extremely large number. Here's the solution:

\[ 3^{274} = 103438383280696835284772024672334899474875005663381728568994430149145171019164787602209635749093303887808693298763169244531588102118034487780233101 \]

This is a 131-digit number.

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Here are 5 related questions:

1. What is \( 3^{100} \)?
2. How do you calculate large powers efficiently using modular arithmetic?
3. What is the result of \( 3^{274} \mod 1000 \)?
4. How do logarithms help in dealing with large exponentiation?
5. What are some real-life applications of large exponentiation?

**Tip:** When dealing with very large numbers, consider using logarithms to simplify calculations.

Explore how to calculate 3 raised to the power of 274 with a detailed solution. Understand exponential growth and the impact of large numbers. Suitable for advanced high school students and enthusiasts of mathematical computation.

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