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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 π ≥ 0, the square root π is a real number s such that π ≥ 0 and π ! = π 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 πth roots. ! ! π₯ β ! π¦ = ! !" ! = ! −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 π and π with π > 0, if π ! is a real number, then ! ! ! ! ! π != π ! = π ! Why does the definition include the restriction that π ! is a real number? For You to Do Evaluate the following expression: ! ! ! ! a. 27 β 27 ! !" ! b. ! !" ! Homework: p. 30-­β32 #1, 5, 6 p. 56 #2, 4, 9-­β11, 13 ! ! c. 16!