Getting Started 
Misconception/Error The student does not understand the relationship between radicals and rational exponents. 
Examples of Student Work at this Level The student:
 Interprets the exponent as a coefficient (e.g., rewrites Â as Â andÂ Â asÂ ).
 Interprets the numerator of the exponent as a coefficient (e.g., rewrites Â as .
 Uses the denominator of the rational exponent as a coefficient of the radical (e.g., rewrites Â as ).

Questions Eliciting Thinking What does 5^{2} mean? What does Â mean?
What is meant by the index of a radical? What does the index mean? 
Instructional Implications If needed, review related terminology such as radical, radicand, index, exponent, base, and power. Also, review the properties of exponents. Review the meaning of the index of a radical and how to represent a radical such as Â or Â in equivalent exponential form. Ask the student to revise the responses to the first two questions.
Explain the definition of rational exponents and provide examples of expressions written in both radical and exponential form. Ask the student to revise the response to the third question. Model rewritingÂ Â as Â or . Review the meaning of a negative exponent and allow the student to revise the response to the fourth problem. Provide additional examples of numerical and variable expressions written in exponential form and ask the student to rewrite each in an equivalent radical form. 
Moving Forward 
Misconception/Error The student interchanges the index and the power in the rational exponent when the power is different from one. 
Examples of Student Work at this Level The student rewritesÂ Â as Â Â andÂ Â as . However, the student rewritesÂ Â as Â and Â as .

Questions Eliciting Thinking What does the numerator of the rational exponent mean? What does the denominator of the rational exponent mean?
Can you simplify ? What would you do first? Then what? 
Instructional Implications Review the definition of rational exponents and provide examples of expressions written in both radical and exponential form. Remind the student that Â so Â or . If needed, review the meaning of a negative exponent and allow the student to revise the response to the fourth problem. Provide additional examples of numerical and variable expressions written in exponential form and ask the student to rewrite each in an equivalent radical form. 
Almost There 
Misconception/Error The student errs when working with negative exponents. 
Examples of Student Work at this Level The student correctly rewrites the first three expressions in radical form. However, the student rewrites Â incorrectly.

Questions Eliciting Thinking What does a negative exponent mean? Can you rewriteÂ Â in an equivalent form with a positive exponent? 
Instructional Implications Review the properties of exponents (in particular, the quotient rule). Show the student an expression such as: Â which is equivalent to . Then use the quotient rule to simplifyÂ Â as . Explain that Â must equal Â in order for the properties of exponents to apply to integer exponents, and extending the properties of exponents to integer exponents allows for a definition of negative exponents. Guide the student to rewriteÂ Â as Â and then as .
Provide additional examples of numerical and variable expressions written in exponential form and ask the student to rewrite each in an equivalent radical form. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student correctly rewrites each expression in radical form.

Questions Eliciting Thinking How would you describe, in general, the relationship between rational exponents and the radical notation?
Why do you suppose taking a square root of a number is equivalent to raising the number to the onehalf power? 
Instructional Implications Challenge the student with additional more complex exponential expressions to convert to radical form.
Consider implementing other MFAS tasks for standard NRN.1.2:Â Rational Exponents  1, Rational Exponents  3, and Rational Exponents  4. 