Lesson 3Powers of Powers of 10
Learning Goal
Let’s look at powers of powers of 10.
Learning Targets
I can explain and use a rule for raising a power of 10 to a power.
Lesson Terms
- base (of an exponent)
Warm Up: Big Cube
Problem 1
What is the volume of a giant cube that measures 10,000 km on each side?
Activity 1: Taking Powers of Powers of 10
Problem 1
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.
expression
expanded
single power of 10
If you chose to skip one entry in the table, which entry did you skip? Why?
Problem 2
Use the patterns you found in the table to rewrite
Problem 3
If you took the amount of oil consumed in 2 months in 2013 worldwide, you could make a cube of oil that measures
Activity 2: How Do the Rules Work?
Problem 1
Andre and Elena want to write
Andre says, “When you multiply powers with the same base, it just means you add the exponents, so
.” Elena says, “
is multiplied by itself 3 times, so .”
Do you agree with either of them? Explain your reasoning.
Are you ready for more?
Problem 1
Lesson Summary
In this lesson, we developed a rule for taking a power of 10 to another power: Taking a power of 10 and raising it to another power is the same as multiplying the exponents.
See what happens when raising
This works for any power of powers of 10. For example,