In this activity, students will substitute numbers from a given list into an expression with a fractional exponent to discover the connection between rational exponents and radicals.
As an introduction to rational exponents, students will discover the rule that a fractional exponent is the same as finding a root of a number.
Before the Activity
Students should have previous experience simplifying square roots, cube roots, and nth roots. Students also need previous experience writing conjectures based upon numerical observations.
During the Activity
Each student should have the RationalExponents.tns file on the Nspire handheld.
Students should work though the document in pairs or small groups, writing down their conjectures on the handout along with the numeric solutions or on a separate sheet of paper as notes.
At the end of the activity, have groups share their conjectures and explanations. From this point, the lesson should continue with rational expressions containing variables.