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Unit 7 - Lesson 3 - Grade 8: Illustrative Mathematics

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Grade 8 Unit 7
Lesson 3: Powers of Powers of 10
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 7
Lesson 3: Powers of Powers of 10
CC BY 2021 Illustrative Mathematics®
Lesson: Powers of Powers of 10

Big Cube (Warm Up)

1.

What is the volume of a giant cube that measures 10,000 km on each side?

Raising Powers of 10 to Another Power

2.

  • Complete the table to explore patterns in the exponents when raising a power of 10 to a power. You may skip a single box in the table, but if you do, be prepared to explain why you skipped it.
  • If you chose to skip one entry in the table, which entry did you skip? Why?


3.

Use the patterns you found in the table to rewrite (10m)n as an equivalent expression with a single exponent, like 10▢.

4.

If you took the amount of oil consumed in 2 months in 2013 worldwide, you could make a cube of oil that measures 103 meters on each side. How many cubic meters of oil is this? Do you think this would be enough to fill a pond, a lake, or an ocean?


How Do the Rules Work?

Andre and Elena want to write 102 · 102 · 102 with a single exponent.

Andre says, “When you multiply powers with the same base, it just means you add the exponents, so 102 · 102 · 102 = 102+2+2 = 106.”

Elena says, “ 102 is multiplied by itself 3 times, so 102 · 102 · 102 = (102)3 = 102+3 = 105."
5.

Do you agree with either of them? Explain your reasoning.

Cool Down: Making a Million

Making a Million

Here are some equivalent ways of writing 104.
  • 10,000
  • 10 · 103
  • (102)2
6.

Write as many expressions as you can that have the same value as 106. Focus on using exponents and multiplication.