The image shows a mathematical problem that involves converting the number $(523)_6$ from base 6 to base 9.

To solve this, we'll follow these steps:

1. Convert the base-6 number to base 10 (decimal):

   $(523)_6 = 5 \times 6^2 + 2 \times 6^1 + 3 \times 6^0$

   Calculate each term: $5 \times 6^2 = 5 \times 36 = 180$ $2 \times 6^1 = 2 \times 6 = 12$ $3 \times 6^0 = 3 \times 1 = 3$

   Now, add them together: $180 + 12 + 3 = 195$ So, $(523)_6 = 195$ in decimal (base 10).

2. Convert the decimal number 195 to base 9:

   To convert 195 to base 9, divide the number by 9 and keep track of the remainders:

   $195 \div 9 = 21 \text{ with a remainder of } 6$ $21 \div 9 = 2 \text{ with a remainder of } 3$ $2 \div 9 = 0 \text{ with a remainder of } 2$

   Reading the remainders from bottom to top, $195$ in base 10 is $(236)_9$.

So, the conversion of $(523)_6$ to base 9 gives $(236)_9$.

Would you like any details or have any questions?

Here are five related questions:

1. How do you convert a base-8 number to base-5?
2. What is the significance of different number bases in computer science?
3. Can you explain how to convert a number from base-16 to base-2?
4. What is the process for converting a decimal number to a base-7 number?
5. Why do we use base-10 (decimal) in everyday life?

Tip: When converting between bases, converting first to base 10 (decimal) is often the easiest approach, especially when the base is not a power of 2.