# Exponent Law: Geometric Illustration

- Author:
- Tim Brzezinski

- Topic:
- Algebra, Exponent, Mathematics

**red point**and

**purple point**each time before re-sliding the slider. (For this illustration, assume lines that appear to be parallel

*are*parallel.) After doing so, please answer the questions that follow.

## 1.

What can we conclude about the area of the **green rectangle** and the area of the **yellow rectangle**? Why can we conclude this?

## 2.

Why does the area of the **green rectangle** never change (despite the transformations we see)?

## 3.

**Suppose the length of the purple segment = 2. **
**Suppose the length of the red segment = 3. **
What would the length of the **single-tick segment** be (in terms of *a*)?
What would the length of the **double-tick segment** be (in terms of *a*)?

## 4.

Given the information in (3), what would the length of the vertical segment (farthest to the right) be? (Express in terms of *a*).

## 5.

Given your response for (1), write a relationship (equation) that contains the expressions you wrote for (3) and (4) above.

## 6.

In general, what property (law) of exponents does this animation help illustrate? Explain.