Solutions to Try Its

1. a. [latex]{k}^{15}[/latex]
b. [latex]{\left(\frac{2}{y}\right)}^{5}[/latex]
c. [latex]{t}^{14}[/latex]

2. a. [latex]{s}^{7}[/latex]
b. [latex]{\left(-3\right)}^{5}[/latex]
c. [latex]{\left(e{f}^{2}\right)}^{2}[/latex]

3. a. [latex]{\left(3y\right)}^{24}[/latex]
b. [latex]{t}^{35}[/latex]
c. [latex]{\left(-g\right)}^{16}[/latex]

4. a. [latex]1[/latex]
b. [latex]\frac{1}{2}[/latex]
c. [latex]1[/latex]
d. [latex]1[/latex]

5. a. [latex]\frac{1}{{\left(-3t\right)}^{6}}[/latex]
b. [latex]\frac{1}{{f}^{3}}[/latex]
c. [latex]\frac{2}{5{k}^{3}}[/latex]

6. a. [latex]{t}^{-5}=\frac{1}{{t}^{5}}[/latex]
b. [latex]\frac{1}{25}[/latex]

7. a. [latex]{g}^{10}{h}^{15}[/latex]
b. [latex]125{t}^{3}[/latex]
c. [latex]-27{y}^{15}[/latex]
d. [latex]\frac{1}{{a}^{18}{b}^{21}}[/latex]
e. [latex]\frac{{r}^{12}}{{s}^{8}}[/latex]

8. a. [latex]\frac{{b}^{15}}{{c}^{3}}[/latex]
b. [latex]\frac{625}{{u}^{32}}[/latex]
c. [latex]\frac{-1}{{w}^{105}}[/latex]
d. [latex]\frac{{q}^{24}}{{p}^{32}}[/latex]
e. [latex]\frac{1}{{c}^{20}{d}^{12}}[/latex]

9. a. [latex]\frac{{v}^{6}}{8{u}^{3}}[/latex]
b. [latex]\frac{1}{{x}^{3}}[/latex]
c. [latex]\frac{{e}^{4}}{{f}^{4}}[/latex]
d. [latex]\frac{27r}{s}[/latex]
e. [latex]1[/latex]
f. [latex]\frac{16{h}^{10}}{49}[/latex]

10. a. [latex]$1.52\times {10}^{5}[/latex]
b. [latex]7.158\times {10}^{9}[/latex]
c. [latex]$8.55\times {10}^{13}[/latex]
d. [latex]3.34\times {10}^{-9}[/latex]
e. [latex]7.15\times {10}^{-8}[/latex]

11. a. [latex]703,000[/latex]
b. [latex]-816,000,000,000[/latex]
c. [latex]-0.00000000000039[/latex]
d. [latex]0.000008[/latex]

12. a. [latex]-8.475\times {10}^{6}[/latex]
b. [latex]8\times {10}^{-8}[/latex]
c. [latex]2.976\times {10}^{13}[/latex]
d. [latex]-4.3\times {10}^{6}[/latex]
e. [latex]\approx 1.24\times {10}^{15}[/latex]

13. Number of cells: [latex]3\times {10}^{13}[/latex]; length of a cell: [latex]8\times {10}^{-6}[/latex] m; total length: [latex]2.4\times {10}^{8}[/latex] m or [latex]240,000,000[/latex] 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 [latex]{2}^{3}[/latex] is the same as [latex]2\times 2\times 2[/latex], which is 8. [latex]{3}^{2}[/latex] is the same as [latex]3\times 3[/latex], which is 9.

3. It is a method of writing very small and very large numbers.

5. 81

7. 243

9. [latex]\frac{1}{16}[/latex]

11. [latex]\frac{1}{11}[/latex]

13. 1

15. [latex]{4}^{9}[/latex]

17. [latex]{12}^{40}[/latex]

19. [latex]\frac{1}{{7}^{9}}[/latex]

21. [latex]3.14\times {10}^{-5}[/latex]

23. 16,000,000,000

25. [latex]{a}^{4}[/latex]

27. [latex]{b}^{6}{c}^{8}[/latex]

29. [latex]a{b}^{2}{d}^{3}\\[/latex]

31. [latex]{m}^{4}[/latex]

33. [latex]\frac{{q}^{5}}{{p}^{6}}[/latex]

35. [latex]\frac{{y}^{21}}{{x}^{14}}[/latex]

37. [latex]25[/latex]

39. [latex]72{a}^{2}[/latex]

41. [latex]\frac{{c}^{3}}{{b}^{9}}[/latex]

43. [latex]\frac{y}{81{z}^{6}}[/latex]

45. 0.00135 m

47. [latex]1.0995\times {10}^{12}[/latex]

49. 0.00000000003397 in.

51. 12,230,590,464 [latex]{m}^{66}[/latex]

53. [latex]\frac{{a}^{14}}{1296}[/latex]

55. [latex]\frac{n}{{a}^{9}c}[/latex]

57. [latex]\frac{1}{{a}^{6}{b}^{6}{c}^{6}}[/latex]

59. 0.000000000000000000000000000000000662606957