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The problem is asking to order a list of expressions from least to greatest. The expressions provided are:

- \( 40^2 \)
- \( 8^3 \)
- \( 10^3 \)
- \( 7.8^2 \)
- \( 10^4 \)

Let's evaluate each one:

1. \( 40^2 = 40 \times 40 = 1600 \)
2. \( 8^3 = 8 \times 8 \times 8 = 512 \)
3. \( 10^3 = 10 \times 10 \times 10 = 1000 \)
4. \( 7.8^2 = 7.8 \times 7.8 = 60.84 \)
5. \( 10^4 = 10 \times 10 \times 10 \times 10 = 10000 \)

Now we can order them from least to greatest:
- \( 7.8^2 = 60.84 \)
- \( 8^3 = 512 \)
- \( 10^3 = 1000 \)
- \( 40^2 = 1600 \)
- \( 10^4 = 10000 \)

The correct order from least to greatest is:
1. \( 7.8^2 \)
2. \( 8^3 \)
3. \( 10^3 \)
4. \( 40^2 \)
5. \( 10^4 \)

Would you like further clarification or details on any of the steps?

Here are five related questions:
1. How do exponents affect the growth rate of a number?
2. What are the differences between squaring and cubing a number?
3. How does \( 10^n \) change as \( n \) increases?
4. What other methods can we use to compare large powers?
5. How would adding more terms to the exponent affect the comparisons?

**Tip:** When comparing expressions with exponents, evaluate each term carefully, especially when exponents differ in base or power!

Here is a list of expressions. Order them from least to greatest: 40^2, 8^3, 10^3, 7.8^2, 10^4.

This problem involves ordering expressions with exponents from least to greatest. It includes expressions like 40^2, 8^3, 10^3, 7.8^2, and 10^4. The step-by-step solution shows how to compare these powers and evaluate them correctly. Suitable for students in Grades 6-8.

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