# Lesson 1

Reviewing Exponents

- Let’s review exponents.

### 1.1: Reviewing Exponents

Complete the table.

expanded form | exponential form |
---|---|

\(2\boldcdot2\boldcdot2\) | \(2^3\) |

\(3\boldcdot3\boldcdot3\boldcdot3\) | |

\(5^2\) | |

\(x\boldcdot x\boldcdot x\boldcdot x\boldcdot x\boldcdot x\boldcdot x\) | |

\(y^3\) | |

\(\left(x\boldcdot y\right)^2\) |

### 1.2: Saving Money

Clare has a summer job. She wants to save money to spend on the family vacation at the end of summer. She is going to save $5 per week for each of the 10 weeks she is working.

Tyler also has a summer job and he, too, would like to save money to spend on the family vacation. He is going to start by saving $2 the first and second weeks and double the amount he saves each of the other weeks he is working ($4 the third week, $8 the fourth week, and so on).

Complete the table showing how much money each of them will have at the end of each week for the 10 weeks.

week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | \(x \) |
---|---|---|---|---|---|---|---|---|---|---|---|

Clare | 5 | 10 | 15 | ||||||||

Tyler | 2 | 4 | 8 |

### 1.3: Identifying Equivalent Expressions

Choose an expression from List A and match it with an equivalent expression from List B and from List C.

- For each match that you find, explain to your partner how you know it’s a match.
- For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
- Switch roles so that your partner chooses a different expression from List A and matches it with an equivalent expression from List B and from List C.

List A

\(8\boldcdot8\boldcdot8\)

\(9\boldcdot27\boldcdot3\)

\(10\boldcdot100\)

\(\frac{1}{4}\boldcdot\frac{1}{4}\boldcdot\frac{1}{2}\)

\(3+3+3+3+3+3\)

List B

\(10^3\)

\(6 \boldcdot 3\)

\(\left(\frac{1}{2}\right)^5\)

\(3^2\boldcdot3^4\)

\(2^3\boldcdot4^3\)

List C

18

\(\frac{1}{32}\)

512

729

1,000