In this Warm-up, students practice using exponent rules to find a missing exponent. The rule is applied to a value with a fractional exponent, which can be done even though students have not encountered such exponents before. Noticing how the fractional exponents work, using the exponent rule, will help make the connection to roots easier later in the lesson.

Students must use the structure of the equations to find the missing values (MP7).

• “Although we have not seen exponents as fractions before, how did you find the answer to the last question?” (Using the exponent rule, I knew that the exponents should be multiplied together, and .)
• “Can you see how the  might be related to the last question? Explain your reasoning.” ( and )

In this activity, students are led through a series of questions that help them notice that both and , which shows that there is a connection between a root and a value with a fractional exponent. They then practice rewriting a few values using the equivalence.

This activity focuses on unit fractions in the exponent.

In this partner activity, students take turns rewriting values as roots, with fractional exponents, and as their numerical value. As students trade roles, explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

There are many possible solutions to the last row of the table, so monitor for different correct answers that students may provide.

The focus of the activity is connecting the first 2 columns. If students would benefit from the use of calculators or other technology to find the numerical values, make them available for students to use (MP5).