# Lesson 12: Meaning of Exponents

Let’s see how exponents show repeated multiplication.

## 12.1: Notice and Wonder: Dots and Lines

What do you notice? What do you wonder?

## 12.2: The Genie’s Offer

You are walking along and you find a brass bottle that looks really, really old. There appears to be some writing on the bottle! You try to clean off some dirt to read it better. A genie appears! He is so happy to be free. He wants to repay you. He offers two ways to repay you and you must choose one:

• He will give you \$50,000; or • He will give you one magical \$1 coin. The magic coin will turn into 2 coins on the first day. The 2 coins will turn into 4 coins on the second day. On the third day, the 4 coins will magically turn into 8 coins. The genie explains that the magic coins will continue this pattern for 28 days.
1. The number of coins on the third day will be $2 \boldcdot 2 \boldcdot 2$. Can you write another expression using exponents for the number of coins there will be on the third day?
2. What do $2^5$ and $2^6$ represent in this situation? Evaluate $2^5$ and $2^6$ without a calculator.