What is the volume of a giant cube that measures 10,000 km on each side? Be prepared to explain your reasoning.
3.2
Activity
Raising Powers of 10 to Another Power
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?
Use the patterns you found in the table to rewrite as an equivalent expression with a single exponent, like .
If you took the amount of oil consumed in 2 months in 2013 worldwide, you could make a cube of oil that measures 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?
Student Lesson Summary
In this lesson, we developed a rule for raising 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.
To understand this, take and raise it to the power of 3. We know that has two factors that are 10. Raising to the power of 3 means that there are three groups of two factors that are 10, for a total of 6 factors that are 10, or .
This works for any power of 10 raised to another power. For example, .
Glossary
None
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