Convert the base  
7
  number  
5624
7
  to base  
10
 . Do not include the subscript  
10
  in your answer.

To convert the base 7 number \( 5624_7 \) to base 10, follow these steps:

Each digit is multiplied by 7 raised to the power of its position (counting from right to left, starting at 0).

\[
5624_7 = 5 \cdot 7^3 + 6 \cdot 7^2 + 2 \cdot 7^1 + 4 \cdot 7^0
\]

Now calculate each term:

\[
5 \cdot 7^3 = 5 \cdot 343 = 1715
\]
\[
6 \cdot 7^2 = 6 \cdot 49 = 294
\]
\[
2 \cdot 7^1 = 2 \cdot 7 = 14
\]
\[
4 \cdot 7^0 = 4 \cdot 1 = 4
\]

Now, add these values together:

\[
1715 + 294 + 14 + 4 = 2027
\]

So, the base 10 equivalent of \( 5624_7 \) is \( 2027 \).

Would you like any details on this conversion?

Here are five related questions to explore:
1. How would you convert a base 10 number to base 7?
2. What is the base 7 equivalent of the base 10 number 2027?
3. How do you convert base 5 numbers to base 10?
4. What are common strategies for converting between different bases?
5. How do powers of 7 change as you move to higher positions in a number?

**Tip:** When converting from any base to base 10, always multiply each digit by the base raised to the power of its positional index.

Convert the base 7 number 5624_7 to base 10. Do not include the subscript 10 in your answer.

Learn how to convert the base 7 number 5624 to base 10 with a detailed step-by-step solution. This problem involves multiplying digits by powers of 7 and is suitable for students in Grades 8-10 studying number systems and base conversions.

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