1. Is [latex]{2}^{3}[\/latex] the same as [latex]{3}^{2}?[\/latex] Explain.<\/p>\n
2.\u00a0When can you add two exponents?<\/p>\n
3. What is the purpose of scientific notation?<\/p>\n
4. Explain what a negative exponent does.<\/p>\n
For the following exercises, simplify the given expression. Write answers with positive exponents.<\/p>\n
5. [latex]{9}^{2}[\/latex]<\/p>\n
6. [latex]{15}^{-2}[\/latex]<\/p>\n
7. [latex]{3}^{2}\\times {3}^{3}[\/latex]<\/p>\n
8.\u00a0[latex]{4}^{4}\\div 4[\/latex]<\/p>\n
9. [latex]{\\left({2}^{2}\\right)}^{-2}[\/latex]<\/p>\n
10.\u00a0[latex]{\\left(5 - 8\\right)}^{0}[\/latex]<\/p>\n
11. [latex]{11}^{3}\\div {11}^{4}[\/latex]<\/p>\n
12.\u00a0[latex]{6}^{5}\\times {6}^{-7}[\/latex]<\/p>\n
13. [latex]{\\left({8}^{0}\\right)}^{2}[\/latex]<\/p>\n
14.\u00a0[latex]{5}^{-2}\\div {5}^{2}[\/latex]<\/p>\n
For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents.<\/p>\n
15. [latex]{4}^{2}\\times {4}^{3}\\div {4}^{-4}[\/latex]<\/p>\n
16.\u00a0[latex]\\frac{{6}^{12}}{{6}^{9}}[\/latex]<\/p>\n
17. [latex]{\\left({12}^{3}\\times 12\\right)}^{10}[\/latex]<\/p>\n
18.\u00a0[latex]{10}^{6}\\div {\\left({10}^{10}\\right)}^{-2}[\/latex]<\/p>\n
19. [latex]{7}^{-6}\\times {7}^{-3}[\/latex]<\/p>\n
20.\u00a0[latex]{\\left({3}^{3}\\div {3}^{4}\\right)}^{5}[\/latex]<\/p>\n
For the following exercises, express the decimal in scientific notation.<\/p>\n
21. 0.0000314<\/p>\n
22.\u00a0148,000,000<\/p>\n
For the following exercises, convert each number in scientific notation to standard notation.<\/p>\n
23. [latex]1.6\\times {10}^{10}[\/latex]<\/p>\n
24.\u00a0[latex]9.8\\times {10}^{-9}[\/latex]<\/p>\n
For the following exercises, simplify the given expression. Write answers with positive exponents.<\/p>\n
25. [latex]\\frac{{a}^{3}{a}^{2}}{a}[\/latex]<\/p>\n
26.\u00a0[latex]\\frac{m{n}^{2}}{{m}^{-2}}[\/latex]<\/p>\n
27. [latex]{\\left({b}^{3}{c}^{4}\\right)}^{2}[\/latex]<\/p>\n
28.\u00a0[latex]{\\left(\\frac{{x}^{-3}}{{y}^{2}}\\right)}^{-5}[\/latex]<\/p>\n
29. [latex]a{b}^{2}\\div {d}^{-3}[\/latex]<\/p>\n
30.\u00a0[latex]{\\left({w}^{0}{x}^{5}\\right)}^{-1}[\/latex]<\/p>\n
31. [latex]\\frac{{m}^{4}}{{n}^{0}}[\/latex]<\/p>\n
32.\u00a0[latex]{y}^{-4}{\\left({y}^{2}\\right)}^{2}[\/latex]<\/p>\n
33. [latex]\\frac{{p}^{-4}{q}^{2}}{{p}^{2}{q}^{-3}}[\/latex]<\/p>\n
34.\u00a0[latex]{\\left(l\\times w\\right)}^{2}[\/latex]<\/p>\n
35. [latex]{\\left({y}^{7}\\right)}^{3}\\div {x}^{14}[\/latex]<\/p>\n
36.\u00a0[latex]{\\left(\\frac{a}{{2}^{3}}\\right)}^{2}[\/latex]<\/p>\n
37. [latex]{5}^{2}m\\div {5}^{0}m[\/latex]<\/p>\n
38.\u00a0[latex]\\frac{{\\left(16\\sqrt{x}\\right)}^{2}}{{y}^{-1}}[\/latex]<\/p>\n
39. [latex]\\frac{{2}^{3}}{{\\left(3a\\right)}^{-2}}[\/latex]<\/p>\n
40.\u00a0[latex]{\\left(m{a}^{6}\\right)}^{2}\\frac{1}{{m}^{3}{a}^{2}}[\/latex]<\/p>\n
41. [latex]{\\left({b}^{-3}c\\right)}^{3}[\/latex]<\/p>\n
42.\u00a0[latex]{\\left({x}^{2}{y}^{13}\\div {y}^{0}\\right)}^{2}[\/latex]<\/p>\n
43. [latex]{\\left(9{z}^{3}\\right)}^{-2}y[\/latex]<\/p>\n
44.\u00a0To reach escape velocity, a rocket must travel at the rate of [latex]2.2\\times {10}^{6}[\/latex] ft\/min. Rewrite the rate in standard notation.<\/p>\n
45. A dime is the thinnest coin in U.S. currency. A dime\u2019s thickness measures [latex]2.2\\times {10}^{6}[\/latex] m. Rewrite the number in standard notation.<\/p>\n
46.\u00a0The average distance between Earth and the Sun is 92,960,000 mi. Rewrite the distance using scientific notation.<\/p>\n
47. A terabyte is made of approximately 1,099,500,000,000 bytes. Rewrite in scientific notation.<\/p>\n
48.\u00a0The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was [latex]\\$1.71496\\times {10}^{13}[\/latex]. Rewrite the GDP in standard notation.<\/p>\n
49. One picometer is approximately [latex]3.397\\times {10}^{-11}[\/latex] in. Rewrite this length using standard notation.<\/p>\n
50.\u00a0The value of the services sector of the U.S. economy in the first quarter of 2012 was $10,633.6 billion. Rewrite this amount in scientific notation.<\/p>\n
For the following exercises, use a graphing calculator to simplify. Round the answers to the nearest hundredth.<\/p>\n
51. [latex]{\\left(\\frac{{12}^{3}{m}^{33}}{{4}^{-3}}\\right)}^{2}[\/latex]<\/p>\n
52.\u00a0[latex]{17}^{3}\\div {15}^{2}{x}^{3}[\/latex]<\/p>\n
For the following exercises, simplify the given expression. Write answers with positive exponents.<\/p>\n
53. [latex]{\\left(\\frac{{3}^{2}}{{a}^{3}}\\right)}^{-2}{\\left(\\frac{{a}^{4}}{{2}^{2}}\\right)}^{2}[\/latex]<\/p>\n
54.\u00a0[latex]{\\left({6}^{2}-24\\right)}^{2}\\div {\\left(\\frac{x}{y}\\right)}^{-5}[\/latex]<\/p>\n
55. [latex]\\frac{{m}^{2}{n}^{3}}{{a}^{2}{c}^{-3}}\\cdot \\frac{{a}^{-7}{n}^{-2}}{{m}^{2}{c}^{4}}[\/latex]<\/p>\n
56.\u00a0[latex]{\\left(\\frac{{x}^{6}{y}^{3}}{{x}^{3}{y}^{-3}}\\cdot \\frac{{y}^{-7}}{{x}^{-3}}\\right)}^{10}[\/latex]<\/p>\n
57. [latex]{\\left(\\frac{{\\left(a{b}^{2}c\\right)}^{-3}}{{b}^{-3}}\\right)}^{2}[\/latex]<\/p>\n
58.\u00a0Avogadro\u2019s constant is used to calculate the number of particles in a mole. A mole is a basic unit in chemistry to measure the amount of a substance. The constant is [latex]6.0221413\\times {10}^{23}[\/latex]. Write Avogadro\u2019s constant in standard notation.<\/p>\n
59. Planck\u2019s constant is an important unit of measure in quantum physics. It describes the relationship between energy and frequency. The constant is written as [latex]6.62606957\\times {10}^{-34}[\/latex]. Write Planck\u2019s constant in standard notation.<\/p>\n\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t