Question
4 Write the prime factors of these numbers in index form \( \begin{array}{ll}\text { a) } 20 & \text { b) } 96 \text { eog } 2 a)=20 \\ \text { c) } 36 & \text { d) } 100\end{array} \)
Ask by Chen Morgan. in South Africa
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
**Prime Factors in Index Form:**
- **a) 20:** \( 2^{2} \times 5 \)
- **b) 96:** \( 2^{5} \times 3 \)
- **c) 36:** \( 2^{2} \times 3^{2} \)
- **d) 100:** \( 2^{2} \times 5^{2} \)
Solution
Sure! Here are the prime factors of each number written in index (exponent) form:
**a) 20**
\[ 20 = 2^{2} \times 5 \]
**b) 96**
\[ 96 = 2^{5} \times 3 \]
**c) 36**
\[ 36 = 2^{2} \times 3^{2} \]
**d) 100**
\[ 100 = 2^{2} \times 5^{2} \]
---
**Explanation:**
1. **Factorizing 20:**
\[
20 = 2 \times 2 \times 5 = 2^{2} \times 5
\]
2. **Factorizing 96:**
\[
96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^{5} \times 3
\]
3. **Factorizing 36:**
\[
36 = 2 \times 2 \times 3 \times 3 = 2^{2} \times 3^{2}
\]
4. **Factorizing 100:**
\[
100 = 2 \times 2 \times 5 \times 5 = 2^{2} \times 5^{2}
\]
These expressions show each number broken down into its prime components, with exponents indicating the number of times each prime number is used as a factor.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To express the prime factors of the given numbers in index form: a) For 20, the prime factorization is \(2^2 \times 5^1\). b) For 96, it can be broken down into \(2^5 \times 3^1\). c) For 36, the prime factors are \(2^2 \times 3^2\). d) For 100, you can write it as \(2^2 \times 5^2\). The index form condenses the factors nicely, making them easier to work with in calculations!
