Let me analyze the questions in the uploaded image and provide the solutions.

Part (a)

The number $90,357$ is written in expanded form. We break it down into powers of $10$ for each digit:

$(9 \times 10^4) + (0 \times 10^3) + (3 \times 10^2) + (5 \times 10^1) + (7 \times 10^0)$

This is the expanded form of $90,357$.

Part (b)

The number written in expanded form is:

$(7 \times 10^5) + (6 \times 10^3) + (4 \times 10^1) + (8 \times 10^0)$

To write this as a Hindu-Arabic numeral:

• $7 \times 10^5 = 700,000$
• $6 \times 10^3 = 6,000$
• $4 \times 10^1 = 40$
• $8 \times 10^0 = 8$

Adding these together:

$700,000 + 6,000 + 40 + 8 = 706,048$

Thus, the Hindu-Arabic numeral is $706,048$.

Would you like further clarification or detailed steps on these calculations? Here are five questions related to this problem:

1. What is the importance of writing numbers in expanded form?
2. Can you provide an example of another number expanded in this way?
3. How does the positional value of digits affect the expansion process?
4. What are some practical applications of expanded form in mathematics?
5. Can you explain why $10^0 = 1$?

Tip: When working with powers of $10$, remember that the exponent tells you how many places to shift the decimal point!