# Technical Document Extraction: Base 8 Multiplication Problem
## Problem Statement
**Find the product of $6_8 \cdot 7_8$. Express your answer in base 8.**
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## Attempt 1 Analysis
### Steps:
1. **Initial Expression**:
`So we have $6_8 \cdot 7_8`.
*Right.*
2. **Base Conversion**:
- `$6_8 = 6_{10}$`
- `$7_8 = 7_{10}$`
*Right.*
3. **Equation Formation**:
`So our equation becomes $6_{10} \cdot 7_{10}$`.
*Right.*
4. **Multiplication in Base 10**:
`So we have $6_{10} \cdot 7_{10} = 42_{10}$`.
*Right.*
5. **Base 8 Conversion**:
- `$42_{10} \div 8 = 5$ remainder $2$`
- Result: `$52_8$`
*Correct.*
### Final Answer:
`#### 52`
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## Attempt 2 Analysis
### Steps:
1. **Base 10 Expansion**:
- `$6_8 = 6$`
- `$7_8 = 7$`
*Right.*
2. **Multiplication in Base 10**:
`So we get $6 \cdot 7 = 42$`.
*Right.*
3. **Base 8 Conversion**:
- `$42 \div 8 = 5$ remainder $2$`
- Result: `$52_8$`
*Correct.*
### Final Answer:
`#### 52_8`
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## Key Observations
- **No Charts/Diagrams**: The image contains only textual problem-solving steps.
- **Mathematical Notation**:
- Subscripts denote base (e.g., `$6_8$` = 6 in base 8).
- `\cdot` represents multiplication.
- **Correctness**: Both attempts arrive at the same result: `$52_8$`.
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## Conclusion
The problem involves multiplying two base-8 numbers (`$6_8$` and `$7_8$`), converting them to base 10, performing the multiplication, and reconverting the result to base 8. Both attempts confirm the final answer as `$52_8$`.
