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Notes Section P2: Exponents and Radicals This lesson will cover the competencies of the real number system and arithmetic with rational expressions. Summarize the following rules for Properties of Exponents: Let a and b be real numbers and let m and n be integers. 1. am · an = 2. (am)n = 3. (ab)m = 4. a-n = 5. a0 = 6. am = an 7. (a )m = b Ex 1: Evaluate each expression: a. (-3)(-3)5 b. [(-2)3]3 c. (32xy)4 d. 4-3· 43 Ex 2: Simplify and write each expression with positive exponents only: a. r-1· r4 r6 b. 3 m5n · 4m-2n-1 m2n9 9mn2 Ex 3: Simplify and write each expression with positive exponents only: a. 5d-3 b. πβ1 πβ5 c. -20a-2b4 5 a-3b-1 Scientific Notation: Used to help compute with either very ________________ or very___________________ numbers. How do we change a number to scientific notation? What should it look like? Ex 4: Change the following to scientific notation: a. 326,000,000,000 b. 0.000000000000985 Ex 5: Change to standard form: a. 1.345 x 105 b. 4.56 x 10-7 Ex 6: Calculate (3 x 103)(2.5 x 105) Radicals Properties: Use pg 16 in your book to fill in the 6 properties for radicals: 1. 2. 3. 4. 5. 6. Ex 7: Evaluate the following expressions: a. β36 b. - β36 3 c. β d. e. Ex 8: a. b. c. d. 125 64 5 4 β-32 β-81 Simplify each expression: β8 β β2 (3β5)3 3 βx3 6 βy6 An expression involving radicals is in simplest form when the following conditions are satisfied: 1. All possible factors are removed from the radical. 2. All fractions have radical-free denominators. 3. The index of the radical is reduced. Ex 9: Simplify the following: a. 4β48 b. β75x3 c. 4 β(5x4) Ex 10: Simplify: a. 3β24 b. 3 β24a4 c. 3 β-40x6 How can you add or subtract radicals? Ex 11: Combine: a. 2β48 - 3β27 b. 3 β16 - 3β54x4 Rationalizing the denominator: Ex 12: Rationalize the denominator of each expression: a. 5 b. 2 3 2β3 β5 Ex 13: Rationalize 2 3 + β7 Rational exponents: Ex 14: Change the following from radical form to rational exponent form: a. β3 b. 2x 4βx3 Ex 15: Change to radical form: a. (x2 + y2)3/2 b. 2y3/4z1/4 Ex 16: Simplify: a. (-32)-4/5 b. 9 βa3 c. 3 β β125 d. (2x β 1)4/3(2x β 1)-1/3 e. xβ1 (x β 1)-1/2