In this lesson, students use radicals to rewrite expressions with positive bases and positive, rational exponents, such as  as or . They do this by breaking into either or . In the last activity of the lesson, students find rough approximations for numbers written this way by sketching the graph of from integer values of and estimating the -coordinates on that continuous curve for various positive rational -coordinates.

Students reason abstractly and quantitatively when they use exponent rules to reason that two exponential expressions have the same value (MP2).