In this lesson, we developed a rule for multiplying powers of 10: Multiplying powers of 10 corresponds to adding the exponents together. 

To see this, multiply and . We know that has two factors that are 10 and that  has three factors that are 10. That means that has 5 factors that are 10. 

This will work for other powers of 10, too. For example,  .

We also 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, .