1. Is 23 the same as 32? Explain.
2. When can you add two exponents?
3. What is the purpose of scientific notation?
4. Explain what a negative exponent does.
For the following exercises, simplify the given expression. Write answers with positive exponents.
5. 92
6. 15−2
7. 32×33
8. 44÷4
9. (22)−2
10. (5−8)0
11. 113÷114
12. 65×6−7
13. (80)2
14. 5−2÷52
For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents.
15. 42×43÷4−4
16. 69612
17. (123×12)10
18. 106÷(1010)−2
19. 7−6×7−3
20. (33÷34)5
For the following exercises, express the decimal in scientific notation.
21. 0.0000314
22. 148,000,000
For the following exercises, convert each number in scientific notation to standard notation.
23. 1.6×1010
24. 9.8×10−9
For the following exercises, simplify the given expression. Write answers with positive exponents.
25. aa3a2
26. m−2mn2
27. (b3c4)2
28. (y2x−3)−5
29. ab2÷d−3
30. (w0x5)−1
31. n0m4
32. y−4(y2)2
33. p2q−3p−4q2
34. (l×w)2
35. (y7)3÷x14
36. (23a)2
37. 52m÷50m
38. y−1(16x)2
39. (3a)−223
40. (ma6)2m3a21
41. (b−3c)3
42. (x2y13÷y0)2
43. (9z3)−2y
44. To reach escape velocity, a rocket must travel at the rate of 2.2×106 ft/min. Rewrite the rate in standard notation.
45. A dime is the thinnest coin in U.S. currency. A dime’s thickness measures 2.2×106 m. Rewrite the number in standard notation.
46. The average distance between Earth and the Sun is 92,960,000 mi. Rewrite the distance using scientific notation.
47. A terabyte is made of approximately 1,099,500,000,000 bytes. Rewrite in scientific notation.
48. The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was $1.71496×1013. Rewrite the GDP in standard notation.
49. One picometer is approximately 3.397×10−11 in. Rewrite this length using standard notation.
50. The value of the services sector of the U.S. economy in the first quarter of 2012 was $10,633.6 billion. Rewrite this amount in scientific notation.
For the following exercises, use a graphing calculator to simplify. Round the answers to the nearest hundredth.
51. (4−3123m33)2
52. 173÷152x3
For the following exercises, simplify the given expression. Write answers with positive exponents.
53. (a332)−2(22a4)2
54. (62−24)2÷(yx)−5
55. a2c−3m2n3⋅m2c4a−7n−2
56. (x3y−3x6y3⋅x−3y−7)10
57. (b−3(ab2c)−3)2
58. Avogadro’s constant is used to calculate the number of particles in a mole. A mole is a basic unit in chemistry to measure the amount of a substance. The constant is 6.0221413×1023. Write Avogadro’s constant in standard notation.
59. Planck’s constant is an important unit of measure in quantum physics. It describes the relationship between energy and frequency. The constant is written as 6.62606957×10−34. Write Planck’s constant in standard notation.
Licenses & Attributions
CC licensed content, Specific attribution
College Algebra.Provided by: OpenStaxAuthored by: OpenStax College Algebra.Located at: https://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface.License: CC BY: Attribution.