Solutions to Try Its

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

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

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

4. a. $1$
b. $\frac{1}{2}$
c. $1$
d. $1$

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

6. a. ${t}^{-5}=\frac{1}{{t}^{5}}$
b. $\frac{1}{25}$

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

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

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

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

11. a. $703,000$
b. $-816,000,000,000$
c. $-0.00000000000039$
d. $0.000008$

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

13. Number of cells: $3\times {10}^{13}$; length of a cell: $8\times {10}^{-6}$ m; total length: $2.4\times {10}^{8}$ 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 ${2}^{3}$ is the same as $2\times 2\times 2$, which is 8. ${3}^{2}$ is the same as $3\times 3$, which is 9.

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

5. 81

7. 243

9. $\frac{1}{16}$

11. $\frac{1}{11}$

13. 1

15. ${4}^{9}$

17. ${12}^{40}$

19. $\frac{1}{{7}^{9}}$

21. $3.14\times {10}^{-5}$

23. 16,000,000,000

25. ${a}^{4}$

27. ${b}^{6}{c}^{8}$

29. $a{b}^{2}{d}^{3}\\$

31. ${m}^{4}$

33. $\frac{{q}^{5}}{{p}^{6}}$

35. $\frac{{y}^{21}}{{x}^{14}}$

37. $25$

39. $72{a}^{2}$

41. $\frac{{c}^{3}}{{b}^{9}}$

43. $\frac{y}{81{z}^{6}}$

45. 0.00135 m

47. $1.0995\times {10}^{12}$

49. 0.00000000003397 in.

51. 12,230,590,464 ${m}^{66}$

53. $\frac{{a}^{14}}{1296}$

55. $\frac{n}{{a}^{9}c}$

57. $\frac{1}{{a}^{6}{b}^{6}{c}^{6}}$

59. 0.000000000000000000000000000000000662606957