https://file.aiquickdraw.com/mathbot/file/1727240994511103mq9ln.jpg

The question in the image is in Indonesian and translates to:

"How many prime factors are present in the number \( (30)^3 \)?"

### Solution:
First, break down the number \( 30 \) into its prime factors:

\[
30 = 2 \times 3 \times 5
\]

Now, raise this to the power of 3:

\[
(30)^3 = (2 \times 3 \times 5)^3 = 2^3 \times 3^3 \times 5^3
\]

The prime factors of \( (30)^3 \) are \( 2 \), \( 3 \), and \( 5 \). Each prime factor appears with an exponent, but the question asks for the number of **distinct** prime factors. There are 3 distinct prime factors: \( 2 \), \( 3 \), and \( 5 \).

### Answer:
The correct answer is **3**.

Would you like further details or have any questions?

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Here are 5 related questions to expand your understanding:
1. How do you find the prime factors of any number?
2. What are the properties of prime numbers?
3. How does exponentiation affect the prime factorization of a number?
4. Can a composite number have more than one distinct prime factor?
5. How would the prime factorization change if you raised \( 30 \) to a higher power, such as \( 30^5 \)?

**Tip**: Always break down a number into its prime factors before applying exponentiation in problems involving prime factorizations.

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Discover how to determine the number of distinct prime factors in the number (30)^3. This problem involves the fundamental theorem of arithmetic and prime factorization, suitable for students in Grades 6-8.

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