Honors Math 2 Name: Nth Roots and Rational Exponents Date: Warm Up Find each of the following without a calculator. ! ! ! ! 27 16 1 125 Here is our definition of square root. If 𝑟 ≥ 0, the square root 𝑟 is a real number s such that 𝑠 ≥ 0 and 𝑠 ! = 𝑟 Using this as a guide, write a definition for the following: Cubed Root Fourth Root nth Root All the properties of square roots apply to 𝑛th roots. ! ! 𝑥 ∙ ! 𝑦 = ! !" ! = ! −27 Rational Exponents ! What do fractional exponents mean? Start with 8 ! . Can you explain why ! 8 ! = 2? (Hint: Think about your definition of nth root) ! Evaluate 8 ! !! Evaluate 8 ! Definition ! For integers 𝑝 and 𝑞 with 𝑞 > 0, if 𝑎 ! is a real number, then ! ! ! ! ! 𝑎 != 𝑎 ! = 𝑎 ! Why does the definition include the restriction that 𝑎 ! is a real number? For You to Do Evaluate the following expression: ! ! ! ! a. 27 ∙ 27 ! !" ! b. ! !" ! Homework: p. 30-­‐32 #1, 5, 6 p. 56 #2, 4, 9-­‐11, 13 ! ! c. 16!