Unit 7 - Lesson 8 - Grade 8: Illustrative Mathematics

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Grade 8 Unit 7
Lesson 8: Combining Bases
CC BY 2021 Illustrative Mathematics®

Instructions

Grade 8 Unit 7
Lesson 8: Combining Bases
CC BY 2021 Illustrative Mathematics®

Lesson: Combining Bases

Same Exponent, Different Base (Warm Up)

Evaluate 53 · 23

Evaluate 103

Power of Products

The table contains products of expressions with different bases and the same exponent. Complete the table to see how we can rewrite them. Use the “expanded” column to work out how to combine the factors into a new base.

Can you write 23 · 34 with a single exponent? What happens if neither the exponents nor the bases are the same? Explain or show your reasoning.

How Many Ways Can You Make 3,600? (Optional)

Your teacher will give your group tools for creating a visual display to play a game. Divide the display into 3 columns, with these headers: 


How to play:

When the time starts, you and your group will write as many expressions as you can that equal a specific number using one of the exponent rules on your board. When the time is up, compare your expressions with another group to see how many points you earn.
Your group gets 1 point for every unique expression you write that is equal to the number and follows the exponent rule you claimed.
If an expression uses negative exponents, you get 2 points instead of just 1.
You can challenge the other group’s expression if you think it is not equal to the number or if it does not follow one of the three exponent rules.

Cool Down: Help an Absent Student

Help an Absent Student

Using words and equations, explain what you learned about exponents in this lesson so that someone who was absent could read what you wrote and understand the lesson. Consider using an example like 24 · 34 = 64.