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Chapter 8 Coursepack: Exponential and Logarithmic Functions

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Chapter 8 Coursepack: Exponential and Logarithmic Functions Honors Algebra 2 C. Bianchi, 2019 388 Preparation for Chapter 8: Review of Rational Exponents PROPERTIES OF EXPONENTS x a •xb ... = xa + b Multiplying powers: Add exponents b a x x = x a – b Dividing powers: Subtract exponents (x a ) b = x ab Power of a power: Multiply exponents (xy) a = x a y a Power of a product: Distribute the exponent a y x         = b a x x Power of a quotient: Distribute the exponent x -a = a x 1 Negative exponent: Take the reciprocal x 0 = 1 (x ≠ 0) EXAMPLE 1: 7 -2 4 2 3 ( ) xy z − 2 3 5 4 ( )( ) x y x y = 2 1 7 = 3 4 3 2 3 ( )( ) ( ) x y z − = 2 3 5 4 4 ( )( ) ( ) x y x y = 1 49 = 3 12 6 x y z − = 2 3 20 4 x y x y • = 3 12 6 x y z = 22 7 x y Recall that a rational (fractional) exponent represents some type of root (square root, cube root, etc.). EXAMPLE 2: 1 2 81 1 3 ( 8) − 1 4 16 = 81 = 3 −8 = 4 16 = 9 = –2 = 2 DEFINITION OF RATIONAL EXPONENT: 1 n n x x = ( ) m m n n x x = The second definition indicates that the numerator represents a power, while the denominator represents a root. For example, 2 3 27 means taking the second power (square) of a third (cube) root. 389 EXAMPLE 3: 2 3 27 5 4 16 − = ( ) 2 3 27 = 5 4 1 16 = (3)2 = ( ) 5 4 1 16 = 9 = 5 1 2 = 1 32 Simplify each expression as much as possible. There should be no negative exponents in any final answer. Do not use a calculator. 1. 2 13− 2. 2 15− 3. 3 5 − 4. 3 4 − 5. 3 6 7 −       6. 4 5 3 −       7. 3 8 x x • 8. 6 14 x x − • 9. 7 6 ( ) x − 10. 8 9 ( ) x 11. 4 6 3 2 ( ) x y z − 12. 9 6 2 4 ( ) x y z − − 13. 6 3 8 4 ( )( ) x y x y − 14. 3 2 6 5 ( )( ) x y x y − 15. 15 3 8 10 3 x y z x y z − 16. 6 7 13 5 6 x y z x y z − 17. 1 2 196 18. 1 2 289 − 19. 1 3 216 − 20. 1 3 343 21. 3 4 256 22. 4 3 125 23. 2 3 27 − 24. 3 2 16 − 25. 1 1 3 3 4(5) 9(5) + 26. 1 1 4 4 6(7) 8(7) − 27. 1 6 2 (72 ) x 28. 1 10 2 (68 ) x 29. 1 6 3 ( 40 ) − x 30. 1 3 3 ( 56 ) − x 31. 6 4 ( 7) ( 7) x x − − 32. 12 5 ( 3) ( 3) x x + + 33. State the domain restriction for Number 31. 34. State the domain restriction for Number 32. [Show More]

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