The goal of this activity is to help students flexibly transition between different notations for powers of 10 and to introduce the property of multiplication of values with the same base. Students observe patterns in the notations and generalize that  for the values of  and  that are positive integers (MP8).

The goal of this discussion is to reinforce the exponent rule for multiplying exponential expressions with the same base. Introduce and explain the visual display prepared earlier. This display should be kept visible to students throughout the remainder of the unit. 

Continue to reinforce student understanding of this rule by writing out the expanded form of each expression and counting the total number of factors of 10 when discussing the following questions:

• “What is written as a single power of 10?” ()
• “What is written as a single power of 10?” ()
• “What is written as a single power of 10?” ()
• “What are some different ways to write as the product of 2 powers of 10?” ( and )

In this activity, students explore patterns to discover the property for values of and that are positive integers (MP8). 

The goal of this discussion is to reinforce the exponent rule for raising powers of 10 to another power. Introduce and explain the visual display prepared earlier. This display should be kept visible to students throughout the remainder of the unit.

Continue to reinforce student understanding of this rule by writing out an expanded form of each expression when discussing the following questions:

• “What is written as a single power of 10?” ()
• “What is written as a single power of 10?” ( )
• “What are some different ways to write as a power of 10 raised to another power?” (, , )