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Solutions

Solutions to Try Its

1. a. k15{k}^{15} b. (2y)5{\left(\frac{2}{y}\right)}^{5} c. t14{t}^{14} 2. a. s7{s}^{7} b. (3)5{\left(-3\right)}^{5} c. (ef2)2{\left(e{f}^{2}\right)}^{2} 3. a. (3y)24{\left(3y\right)}^{24} b. t35{t}^{35} c. (g)16{\left(-g\right)}^{16} 4. a. 11 b. 12\frac{1}{2} c. 11 d. 11 5. a. 1(3t)6\frac{1}{{\left(-3t\right)}^{6}} b. 1f3\frac{1}{{f}^{3}} c. 25k3\frac{2}{5{k}^{3}} 6. a. t5=1t5{t}^{-5}=\frac{1}{{t}^{5}} b. 125\frac{1}{25} 7. a. g10h15{g}^{10}{h}^{15} b. 125t3125{t}^{3} c. 27y15-27{y}^{15} d. 1a18b21\frac{1}{{a}^{18}{b}^{21}} e. r12s8\frac{{r}^{12}}{{s}^{8}} 8. a. b15c3\frac{{b}^{15}}{{c}^{3}} b. 625u32\frac{625}{{u}^{32}} c. 1w105\frac{-1}{{w}^{105}} d. q24p32\frac{{q}^{24}}{{p}^{32}} e. 1c20d12\frac{1}{{c}^{20}{d}^{12}} 9. a. v68u3\frac{{v}^{6}}{8{u}^{3}} b. 1x3\frac{1}{{x}^{3}} c. e4f4\frac{{e}^{4}}{{f}^{4}} d. 27rs\frac{27r}{s} e. 11 f. 16h1049\frac{16{h}^{10}}{49} 10. a. $1.52\times {10}^{5} b. 7.158×1097.158\times {10}^{9} c. $8.55\times {10}^{13} d. 3.34×1093.34\times {10}^{-9} e. 7.15×1087.15\times {10}^{-8} 11. a. 703,000703,000 b. 816,000,000,000-816,000,000,000 c. 0.00000000000039-0.00000000000039 d. 0.0000080.000008 12. a. 8.475×106-8.475\times {10}^{6} b. 8×1088\times {10}^{-8} c. 2.976×10132.976\times {10}^{13} d. 4.3×106-4.3\times {10}^{6} e. 1.24×1015\approx 1.24\times {10}^{15} 13. Number of cells: 3×10133\times {10}^{13}; length of a cell: 8×1068\times {10}^{-6} m; total length: 2.4×1082.4\times {10}^{8} m or 240,000,000240,000,000 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{2}^{3} is the same as 2×2×22\times 2\times 2, which is 8. 32{3}^{2} is the same as 3×33\times 3, which is 9. 3. It is a method of writing very small and very large numbers. 5. 81 7. 243 9. 116\frac{1}{16} 11. 111\frac{1}{11} 13. 1 15. 49{4}^{9} 17. 1240{12}^{40} 19. 179\frac{1}{{7}^{9}} 21. 3.14×1053.14\times {10}^{-5} 23. 16,000,000,000 25. a4{a}^{4} 27. b6c8{b}^{6}{c}^{8} 29. ab2d3a{b}^{2}{d}^{3}\\ 31. m4{m}^{4} 33. q5p6\frac{{q}^{5}}{{p}^{6}} 35. y21x14\frac{{y}^{21}}{{x}^{14}} 37. 2525 39. 72a272{a}^{2} 41. c3b9\frac{{c}^{3}}{{b}^{9}} 43. y81z6\frac{y}{81{z}^{6}} 45. 0.00135 m 47. 1.0995×10121.0995\times {10}^{12} 49. 0.00000000003397 in. 51. 12,230,590,464 m66{m}^{66} 53. a141296\frac{{a}^{14}}{1296} 55. na9c\frac{n}{{a}^{9}c} 57. 1a6b6c6\frac{1}{{a}^{6}{b}^{6}{c}^{6}} 59. 0.000000000000000000000000000000000662606957

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