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# Solutions

## 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