Rojas Spencer
06/27/2024 · Elementary School
Express each of the following as a product of the powers i) \( 2025=3^{4} \times 5^{2} \) ii) \( 6300=2^{2} \times 3^{2} \times 5^{2} \times 7^{1} \) iii) 6050
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Step-by-step Solution
To express \( 6050 \) as a product of powers of its prime factors, we will first find its prime factorization.
1. **Divide by the smallest prime number (2):**
\[
6050 \div 2 = 3025
\]
So, we have \( 6050 = 2^1 \times 3025 \).
2. **Next, factor \( 3025 \):**
- Check divisibility by \( 3 \): \( 3025 \) is not divisible by \( 3 \).
- Check divisibility by \( 5 \): \( 3025 \div 5 = 605 \).
So, \( 3025 = 5^1 \times 605 \).
3. **Now factor \( 605 \):**
- Check divisibility by \( 5 \): \( 605 \div 5 = 121 \).
So, \( 605 = 5^1 \times 121 \).
4. **Now factor \( 121 \):**
- \( 121 = 11^2 \) (since \( 11 \times 11 = 121 \)).
Putting it all together, we have:
\[
6050 = 2^1 \times 5^2 \times 11^2
\]
Thus, the prime factorization of \( 6050 \) expressed as a product of powers is:
\[
6050 = 2^1 \times 5^2 \times 11^2
\]
Quick Answer
\( 6050 = 2^1 \times 5^2 \times 11^2 \)
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