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The question asks for the "angka satuan" or "unit digit" of \( 777^{777} \). 

To solve this, we need to find the last digit of \( 777^{777} \). However, we can simplify this by focusing on the last digit of the base 777, which is 7. This reduces the problem to finding the last digit of \( 7^{777} \).

### Step-by-step approach:
1. The last digits of powers of 7 repeat in a cycle:
   \[
   \begin{aligned}
   7^1 &\equiv 7 \pmod{10}, \\
   7^2 &\equiv 49 \equiv 9 \pmod{10}, \\
   7^3 &\equiv 343 \equiv 3 \pmod{10}, \\
   7^4 &\equiv 2401 \equiv 1 \pmod{10}.
   \end{aligned}
   \]
   So, the cycle of the last digits of powers of 7 is: \( 7, 9, 3, 1 \).

2. The length of this cycle is 4. To find the last digit of \( 7^{777} \), we determine where \( 777 \) falls in the cycle by finding \( 777 \mod 4 \):
   \[
   777 \div 4 = 194 \text{ remainder } 1.
   \]
   This means \( 777 \equiv 1 \pmod{4} \).

3. Since \( 777 \equiv 1 \pmod{4} \), the last digit of \( 7^{777} \) is the same as the last digit of \( 7^1 \), which is 7.

Thus, the last digit of \( 777^{777} \) is **7**.

The correct answer is C. 7.

Would you like more details or have any other questions? 

Here are some related questions to expand your understanding:
1. What are the unit digits of \( 5^{10} \) and \( 6^{15} \)?
2. How does modular arithmetic help in finding the last digits of large powers?
3. What is the unit digit of \( 3^{1234} \)?
4. Can the unit digit of a number ever change if we add multiples of 10?
5. What patterns can we observe in the last digits of powers of 2?

**Tip**: Whenever solving powers for the last digit, observe if the digits form a repeating cycle; this simplifies the problem greatly!

Solve the problem of finding the unit digit of 777^777 by applying modular arithmetic and recognizing the cyclical pattern of last digits in powers. Suitable for high school students, this problem demonstrates key concepts in number theory and arithmetic patterns.

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