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

Summary