The prime factorization of 6561 is:

\[
6561 = 3^8
\]

### Explanation:

1. Start dividing 6561 by the smallest prime, 3:  
\[
6561 ÷ 3 = 2187
\]
2. Continue dividing by 3:  
\[
2187 ÷ 3 = 729
\]
3. Again:  
\[
729 ÷ 3 = 243
\]
4. Continue:  
\[
243 ÷ 3 = 81
\]
5. Again:  
\[
81 ÷ 3 = 27
\]
6. Continue:  
\[
27 ÷ 3 = 9
\]
7. Finally:  
\[
9 ÷ 3 = 3
\]
8. Divide one more time:  
\[
3 ÷ 3 = 1
\]

Thus, the prime factorization of 6561 is \( 3^8 \).

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. What is the prime factorization of 729?
2. How can prime factorization help in finding the greatest common divisor (GCD)?
3. What is the significance of prime numbers in number theory?
4. How do you find the prime factorization of a composite number using a factor tree?
5. Can every number be written as a product of prime factors?

**Tip:** Prime factorization can be useful in simplifying fractions or solving problems related to divisibility.

Discover the prime factorization of 6561 with a detailed, step-by-step solution. Learn how to repeatedly divide by the prime number 3, resulting in 6561 = 3^8. This breakdown covers essential number theory concepts, including exponents and the Fundamental Theorem of Arithmetic. Perfect for students in Grades 6-8.

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