The purpose of this activity is to extend the definition of non-positive exponents to other bases. Students notice that patterns that were true for powers of 10 also hold for other bases (MP8). 

The goal of this discussion is for students to connect that the exponent rules discovered for powers of 10 work with other bases. Discuss the following questions:

• “How does working with powers of 2 compare to working with powers of 10?” (The rules apply in the same way, but computing the value of some powers of 2 can take longer since we can’t just look at the number of zeros.)
• “What happens when you use exponent rules when one of the exponents is 0?” (The rules apply in the same way. in the same way that .)
• “How does compare to ?” (Both values are positive and less than 1. When each is written as a fraction, has greater numbers in the denominator, so it is less than .)

This activity gives students a chance to practice using exponent rules to analyze expressions and identify equivalent expressions. Students choose 2 out of 4 lists to analyze. As students work, notice the different strategies used to analyze the expressions in each list.

The goal of this discussion is for students to see that the exponent rules are valid for nonzero bases other than 10. For each list, invite students to share which expressions did not match the original expression and to share their reasoning strategies. If necessary for time, consider focusing just on questions 3 and 4 to assess how students have generalized in terms of variables and whether students have internalized the 0 exponent. 

As students share their strategies for each list, discuss: 

• “Do you agree or disagree? Why?”
• “Did anyone think about that expression in a different way?” 
• “Did anyone use the same strategy but would explain it differently?”