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!