https://file.aiquickdraw.com/mathbot/file/1729914982340xhi198jf.jpg

To solve this, let’s break down the given number \( B9BA13_{14} \) into its expanded base-14 form and then convert it to decimal.

### Step 1: Understand Base-14 Digits
In base-14:
- \( B = 11 \)
- \( A = 10 \)

So, \( B9BA13_{14} \) translates to \( 11, 9, 11, 10, 1, 3 \) in decimal digits, from left to right.

### Step 2: Set Up the Expanded Form
The expanded base-14 form for \( B9BA13_{14} \) is:
\[
11 \cdot 14^5 + 9 \cdot 14^4 + 11 \cdot 14^3 + 10 \cdot 14^2 + 1 \cdot 14^1 + 3 \cdot 14^0
\]

### Step 3: Calculate Each Term
Let's compute each term individually:
1. \( 11 \cdot 14^5 = 11 \cdot 537824 = 5916064 \)
2. \( 9 \cdot 14^4 = 9 \cdot 38416 = 345744 \)
3. \( 11 \cdot 14^3 = 11 \cdot 2744 = 30184 \)
4. \( 10 \cdot 14^2 = 10 \cdot 196 = 1960 \)
5. \( 1 \cdot 14^1 = 1 \cdot 14 = 14 \)
6. \( 3 \cdot 14^0 = 3 \cdot 1 = 3 \)

### Step 4: Sum the Terms
Adding these terms together:
\[
5916064 + 345744 + 30184 + 1960 + 14 + 3 = 6293969
\]

### Final Answer
So, \( B9BA13_{14} \) in decimal representation is:
\[
6293969
\]

Let me know if you need further clarification or a breakdown of any steps.

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**Questions to Explore Further:**
1. What are other examples of base-14 numbers and their decimal conversions?
2. How can base-14 be practically useful in different applications?
3. Can this method be applied to bases higher than 14?
4. What is the importance of understanding expanded form in other mathematical bases?
5. How do other numeral systems differ from decimal in terms of calculations?

**Tip:** Always remember that each position in any base system represents a power of that base, starting from the right at \( x^0 \).

Give the expanded base 14 form of B9BA13 in base 14 and convert it to decimal representation.

Learn how to expand and convert the base-14 number B9BA13 into decimal form. This detailed solution covers number systems, base conversions, and calculating powers, suitable for high school students.

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