91 R.8 Radical Expressions CONCEPT PREVIEW Work each problem. 1. Write 23 64 using exponents and evaluate. 2. Write 272/3 in radical form and evaluate. R.8 Exercises 3. (a) 1-3x21/3 (b) 1-3x2-1/3 (c) 13x21/3 (d) 13x2-1/3 4. (a) -3x1/3 (b) -3x-1/3 (c) 3x-1/3 (d) 3x1/3 II A. 32 3 x B. -323 x C. 12 3 3x D. -32 3 x E. 323 x F. 23 -3x G. 23 3x H. 12 3 -3x CONCEPT PREVIEW Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. I CONCEPT PREVIEW Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. 5. 25 t5 6. 26 # 224 7. 250 8. B7 36 9. 32xy - 82xy 10. A2 + 23B A2 - 23B Write each root using exponents and evaluate. See Example 1. 11. 23 125 12. 23 216 13. 24 81 14. 24 256 15. 23 -125 16. 23 -343 17. 24 -81 18. 24 -256 19. 25 32 20. 27 128 21. -25 -32 22. -23 -343 If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent positive real numbers. See Examples 2 and 3. 23. 272/3 24. 323/5 25. -12x1/2 26. -5z2/3 27. m2/3 28. p5/4 29. 12m+ p22/3 30. 15r + 3t24/7 31. 25 k2 32. 24 z5 33. -325p3 34. -m22y5 Find each root. See Example 4. 35. 2122 36. 21-1222 37. 23 x3 38. 27 y7 39. 24 x4 40. 26 x6 41. 225k4m2 42. 24 81p12q4 43. 214x - y22 44. 24 15 + 2m24 45. 2x2 + 6x + 9 46. 2z2 + 20z + 100
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