Standard Form and Expanded Form example showing 8120 in standard form and its expanded form.

The image you've uploaded explains the concepts of standard form and expanded form for numbers. Let's break it down and solve the example given.

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🔹 Standard Form

- This is the usual way we write numbers without using exponents.
- Example: 8120 is in standard form.

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🔹 Expanded Form

- This shows the number as a sum of each digit multiplied by its place value (often using powers of 10).
- In this case, the number 8120 is broken down into:
$$
8000 + 100 + 20
$$

But let’s go deeper and express this fully in expanded form with exponents, which is more precise.

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✔ Step-by-step breakdown of 8120:

We look at each digit and its place value:

| Digit | Place Value | Value |
|-------|-------------|-------|
| 8 | Thousands | 8 × 1000 = 8000 |
| 1 | Hundreds | 1 × 100 = 100 |
| 2 | Tens | 2 × 10 = 20 |
| 0 | Ones | 0 × 1 = 0 |

So,
$$
8120 = 8000 + 100 + 20 + 0
$$

Now, using exponents (powers of 10), we can write:

$$
8120 = 8 \times 10^3 + 1 \times 10^2 + 2 \times 10^1 + 0 \times 10^0
$$

This is the expanded form using exponents.

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✔ Final Answer:

- Standard Form: 8120
- Expanded Form (with exponents):
$$
8 \times 10^3 + 1 \times 10^2 + 2 \times 10^1 + 0 \times 10^0
$$

Or, simplified (without exponents):
$$
8000 + 100 + 20
$$

> Note: The example in the image shows the expanded form without exponents, which is acceptable. But when using exponents, it's more complete and aligns with mathematical notation.

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📌 Summary:

- Standard form: 8120
- Expanded form (no exponents): 8000 + 100 + 20
- Expanded form (with exponents): $ 8 \times 10^3 + 1 \times 10^2 + 2 \times 10^1 + 0 \times 10^0 $

✔ The image correctly shows the concept — just remember that expanded form can include exponents to show place values more formally.