1. a. k15
b. (y2)5
c. t14
2. a. s7
b. (−3)5
c. (ef2)2
3. a. (3y)24
b. t35
c. (−g)16
4. a. 1
b. 21
c. 1
d. 1
5. a. (−3t)61
b. f31
c. 5k32
6. a. t−5=t51
b. 251
7. a. g10h15
b. 125t3
c. −27y15
d. a18b211
e. s8r12
8. a. c3b15
b. u32625
c. w105−1
d. p32q24
e. c20d121
9. a. 8u3v6
b. x31
c. f4e4
d. s27r
e. 1
f. 4916h10
10. a. $1.52\times {10}^{5}
b. 7.158×109
c. $8.55\times {10}^{13}
d. 3.34×10−9
e. 7.15×10−8
11. a. 703,000
b. −816,000,000,000
c. −0.00000000000039
d. 0.000008
12. a. −8.475×106
b. 8×10−8
c. 2.976×1013
d. −4.3×106
e. ≈1.24×1015
13. Number of cells: 3×1013; length of a cell: 8×10−6 m; total length: 2.4×108 m or 240,000,000 m.
Solutions to Odd-Numbered Exercises
1. No, the two expressions are not the same. An exponent tells how many times you multiply the base. So 23 is the same as 2×2×2, which is 8. 32 is the same as 3×3, which is 9.
3. It is a method of writing very small and very large numbers.
5. 81
7. 243
9. 161
11. 111
13. 1
15. 49
17. 1240
19. 791
21. 3.14×10−5
23. 16,000,000,000
25. a4
27. b6c8
29. ab2d3
31. m4
33. p6q5
35. x14y21
37. 25
39. 72a2
41. b9c3
43. 81z6y
45. 0.00135 m
47. 1.0995×1012
49. 0.00000000003397 in.
51. 12,230,590,464 m66
53. 1296a14
55. a9cn
57. a6b6c61
59. 0.000000000000000000000000000000000662606957
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.