From the image, it appears that you are working on converting a base-7 number to decimal values, specifically identifying the place values in a base-7 system and converting them accordingly.

In this problem:

1. Each position represents a power of 7.
2. Starting from the rightmost digit, each position is a power of 7 increasing from $7^0$ to $7^4$ for a five-digit number.
3. You have partially filled out the answers, but one answer (related to $5430_7$) is incorrect, as indicated by the red marking.

Correct Place Values in Base-7:

To convert a number in base-7 to decimal, each digit is multiplied by $7^n$, where $n$ is its position from the right (starting at 0). Here’s a quick guide:

• 7^0 is 1
• 7^1 is 7
• 7^2 is 49
• 7^3 is 343
• 7^4 is 2401

If you're asked to convert 5430 from base-7 to decimal, calculate as follows:

$5 \cdot 343 + 4 \cdot 49 + 3 \cdot 7 + 0 \cdot 1$

Let’s break it down:

• $5 \cdot 343 = 1715$
• $4 \cdot 49 = 196$
• $3 \cdot 7 = 21$
• $0 \cdot 1 = 0$

Now, add these values: $1715 + 196 + 21 + 0 = 1932$

So, 1932 should be the decimal equivalent of $5430_7$.

Would you like more details or further help with other similar questions?

Here are five related questions to expand your understanding:

1. How do you convert other base numbers, like base 5 or base 8, to decimal?
2. What steps are involved in converting decimal numbers to base-7?
3. How does the positional notation work in any base?
4. How would the conversion process differ if we used a six-digit number in base-7?
5. Why do different bases require different place values?

Tip: Always start from the rightmost digit when converting bases to decimal, as it represents the lowest power of the base.