University:
East Georgia State College
Course:
MATH 1113 | Pre-Calculus
Academic year:

2023
Views:

161

Pages:

5
Author:

Clint W.

6.1-6.3 Review Sheet For #1-16: Use the Properties of Exponents to completely simplify the following: 1. (-7)¹ * (-7)³ * (-7)⁴ (-7)⁸ = 7⁸ 2. (6⁶)⁶ 6³⁶ 3. (-4c²)¹¹ -4¹¹c²² 4. x⁹y⁹ / x³y² x⁶y⁷ 5. (-2)⁵ -32 6. 5⁵ * 5⁻¹ 25 7. 3³ / 3⁻³ 3⁶ 8. (5g¹k²)⁻³ 1 / 125g³k⁶ 9. (2²)⁴ 2⁸ 10. (2x⁻²y⁵)(8x¹y⁴) 16xy⁹ 11. 10ab⁴ / 34a⁻¹b⁻⁵ 5a²b⁹ / 17 12. x²y³ * 2x⁴ / 2y³ x⁶ 13. (4a⁴b⁶)(11a⁻²b⁻³) -44a²b³ 14. -4a²b⁻⁶c⁻⁴ / 18a⁻¹b⁻¹c⁻¹ -2a³ / 9b⁵c³ 15. (3x³ / 10y⁻⁷)⁻³ 1000 / 27x⁹y²¹ 16. 4m⁴ / -6m⁻¹n³ * 3n / m² -2m³/n² For #17-22: Write the answer in scientific notation. 17. (2.3 x 10⁻⁴)(9.3 x 10⁴) 21.39 x 10⁰ = 2.139 x 10¹ 18. (5.4 x 10⁻⁵)(1.8 x 10⁻¹) 9.72 x 10⁻⁶ 19. (3.6 x 10⁻⁸)³ 46.656 x 10⁻²⁴ = 4.6656 x 10⁻²³ 20. (5.18 x 10⁻⁵)² 26.8324 x 10⁻¹⁰ = 2.68324 x 10⁻⁹ 21. 2.1 x 10⁻⁴ / 8.4 x 10⁻⁶ 0.25 x 10² = 2.5 x 10¹ 22. 3.6 x 10⁻³ / 4.8 x 10⁻⁷ 0.75 x 10⁴ = 7.5 x 10³ For #23-26: Use direct substitution to evaluate the polynomial function for the given value of x. 23. f(x) = 2x⁵ - 3x⁴ + x³ - 6x + 20 x = 2 f(2) = 2(2)⁵ - 3(2)⁴ + (2)³ - 6(2) + 20 = 32 24. g(x) = 8x³ - 5x² + 14 x = -3 g(-3) = 8(-3)³ - 5(-3)² + 14 = -185 25. f(x) = -2x⁴ - 6x² + 3 x = -5 f(-5) = -2(-5)⁴ - 6(-5)² + 3 = -1397 26. f(x) = 1/2x⁴ - x³ + 10x x = -6 f(-6) = 1/2(-6)⁴ - (-6)³ + 10(-6) = 804 For #27-30: Use synthetic substitution to evaluate the polynomial function for the given value of x. 27. f(x) = 2x⁵ - 3x⁴ + x³ - 6x + 20 x = 2 2 | 2 -3 1 -6 20 | 4 2 6 0 40 ---------------------- 2 1 3 0 4 32 f(2) = 32 28. g(x) = 8x³ - 5x² + 14 x = -3 -3 | 8 -5 0 14 | -24 87 -261 ---------------------- 8 -29 87 -247 g(-3) = -247 29. f(x) = -2x⁴ - 6x² + 3 x = -5 -5 | -2 0 -6 0 3 | 10 -50 280 -1400 ---------------------- -2 10 -56 280 -1397 f(-5) = -1397 30. f(x) = 1/2x⁴ - x³ + 10x x = -6 -6 | 1/2 -1 0 10 0 | -3 24 -144 804 ---------------------- 1/2 -4 24 -134 804 f(-6) = 804 37. Draw a fourth degree polynomial function that has two x-intercepts and a negative leading coefficient. There are several possible answers. 38. Draw a fifth degree polynomial function that has five x-intercepts and a positive leading coefficient. Several possible answers. For #39-42: Find the product. 39. 2x⁴(-3x² + 4x - 1) -6x⁶ + 8x⁵ - 2x⁴ 40. (c+11)(2c²-c-4) 2c³ + 21c² - 15c - 44 41. (x-9)(x²+6x-2) x³ + 6x² - 2x - 9x² - 54x + 18 x³ - 3x² - 56x + 18 42. (2p+1)(6p²-p+8) 12p³ - 2p² + 16p + 6p² - p + 8 12p³ + 4p² + 15p + 8

Math Properties of Exponents Review Key

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