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.

The purpose of the discussion is to draw out the connection that . Select a group to answer the third question and to explain their reasoning.

Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response to the third question. In this structured pairing strategy, students bring their first draft response into conversations with 2–3 different partners. They take turns being the speaker and the listener. As the speaker, students share their initial ideas and read their first draft. As the listener, students ask questions and give feedback that will help clarify and strengthen their partner's ideas and writing.

If time allows, display these prompts for feedback:

• “ makes sense, but what do you mean when you say. . . ?”
• “Can you describe that another way?”
• “How do you know . . . ? What else do you know is true?”

Close the partner conversations, and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words they got from their partners to make their next draft stronger and clearer. If time allows, invite students to compare their first and final drafts. Select 2–3 students to share how their drafts changed and why they made the changes they did.

Ask students, “How can you rewrite as an exponential expression?” ()

Add to the classroom display the rule .

Then select groups to show how this rule can be used to answer the remaining questions.

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).

The purpose of the discussion is for students to share their insights and struggles with writing values in equivalent forms. Invite students to share how they found equivalent values in the missing forms.

• “What are some ways you handled the last row?”
• “Describe any difficulties you experienced and how you resolved them.”