You are asking to calculate \( 562741_8 \times 5_8 \) in base 8. Let's break this down step by step.

### Step 1: Convert both numbers from base 8 to base 10.

- The first number is \( 562741_8 \), which means we convert it to base 10:
  \[
  562741_8 = 5 \times 8^5 + 6 \times 8^4 + 2 \times 8^3 + 7 \times 8^2 + 4 \times 8^1 + 1 \times 8^0
  \]
  Let's calculate this.

- The second number is \( 5_8 \), which is already a base 10 number:
  \[
  5_8 = 5_{10}
  \]

### Step 2: Multiply the two base 10 numbers.

After converting \( 562741_8 \) to base 10, we multiply that result by 5.

### Step 3: Convert the result back to base 8.

Let me perform the calculations for you.### Solution:

1. Convert \( 562741_8 \) to base 10:
   \[
   562741_8 = 189921_{10}
   \]

2. Multiply by 5 (in base 10):
   \[
   189921 \times 5 = 949605_{10}
   \]

3. Convert the result \( 949605_{10} \) back to base 8:
   \[
   949605_{10} = 3476545_8
   \]

Thus, the result of \( 562741_8 \times 5_8 \) in base 8 is \( 3476545_8 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you convert a base 8 number to base 16?
2. Can you multiply two base 8 numbers without converting them to base 10 first?
3. What is the general method for converting from any base \( n \) to base \( m \)?
4. How can you add two numbers in base 8 directly?
5. What are some practical uses of base 8 calculations?

**Tip:** When converting between bases, it's helpful to break down each step carefully to avoid errors, especially when working with unfamiliar bases like base 8!

Learn how to multiply two numbers in base 8, 562741_8 and 5_8, by converting to base 10 and back. This detailed step-by-step solution includes essential formulas and methods for base conversions and multiplication. Ideal for Grades 9-11 students studying number systems.

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