The image you provided explains negative exponents and includes a table for converting expressions with negative exponents into their standard form. Let's go through the table and fill in the missing entries based on the pattern:

Table Overview

• The table shows how to represent exponents as a division and then transition to their standard form.
• Every time you divide by 10, the exponent decreases by one.

Filled Table

Explanation

• Positive Exponents: $10^3$, $10^2$, and $10^1$ represent 1000, 100, and 10, respectively.
• Zero Exponent: $10^0$ equals 1.
• Negative Exponents: $10^{-1}$, $10^{-2}$, and $10^{-3}$ represent 0.1, 0.01, and 0.001, respectively.

This shows that negative exponents represent fractions or decimal values that are the reciprocal of the positive exponent.

Do you want further details on this topic, or do you have any questions?

Here are 5 related questions to explore further:

1. What happens if the exponent is negative and not an integer (e.g., $10^{-1.5}$)?
2. How do you multiply and divide numbers with negative exponents?
3. Can negative exponents be applied to variables, and how would you simplify such expressions?
4. What is the significance of $10^{-n}$ in scientific notation?
5. How would you solve an equation that involves negative exponents?

Tip: Always remember that a negative exponent indicates that you should take the reciprocal of the base raised to the corresponding positive exponent.