{"id":15814,"date":"2019-07-30T15:36:25","date_gmt":"2019-07-30T15:36:25","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/exponents-and-scientific-notation\/"},"modified":"2022-02-05T00:40:16","modified_gmt":"2022-02-05T00:40:16","slug":"problem-set-exponents-and-scientific-notation","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/problem-set-exponents-and-scientific-notation\/","title":{"raw":"Problem Set: Exponents and Scientific Notation","rendered":"Problem Set: Exponents and Scientific Notation"},"content":{"raw":"
\r\n

PROBLEM SET<\/h3>\r\n
\r\n

For the following exercises, simplify the given expression. Write answers with positive exponents.<\/p>\r\n\r\n

\r\n
\r\n

1. [latex]\\frac{{a}^{3}{a}^{2}}{a}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"295882\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"295882\"][latex]{a}^{4}[\/latex][\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

2. [latex]\\frac{m{n}^{2}}{{m}^{-2}}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

3.\u00a0[latex]{\\left({b}^{3}{c}^{4}\\right)}^{2}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"718985\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"718985\"][latex]{b}^{6}{c}^{8}[\/latex][\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

4.\u00a0[latex]{\\left(\\frac{{x}^{-3}}{{y}^{2}}\\right)}^{-5}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

5.\u00a0[latex]a{b}^{2}\u00f7{d}^{-3}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"814001\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"814001\"][latex]a{b}^{2}{d}^{3}[\/latex][\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

6.\u00a0[latex]{\\left({w}^{0}{x}^{5}\\right)}^{-1}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

7.\u00a0[latex]\\frac{{m}^{4}}{{n}^{0}}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"757897\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"757897\"][latex]{m}^{4}[\/latex][\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

8.\u00a0[latex]{y}^{-4}{\\left({y}^{2}\\right)}^{2}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

9.\u00a0[latex]\\frac{{p}^{-4}{q}^{2}}{{p}^{2}{q}^{-3}}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"122516\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"122516\"][latex]\\frac{{q}^{5}}{{p}^{6}}[\/latex][\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

10.\u00a0[latex]{\\left(l \\cdot w \\right)}^{2}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

11.\u00a0[latex]{\\left({y}^{7}\\right)}^{3}\u00f7{x}^{14}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"932867\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"932867\"][latex]\\frac{{y}^{21}}{{x}^{14}}[\/latex][\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

12.\u00a0[latex]{\\left(\\frac{a}{{2}^{3}}\\right)}^{2}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

13.\u00a0[latex]{5}^{2}m\u00f7{5}^{0}m[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"142963\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"142963\"]25[\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

14.\u00a0[latex]\\frac{{\\left(16\\sqrt{x}\\right)}^{2}}{{y}^{-1}}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

15.\u00a0[latex]\\frac{{2}^{3}}{{\\left(3a\\right)}^{-2}}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"704640\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"704640\"][latex]72{a}^{2}[\/latex][\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

16.\u00a0[latex]{\\left(m{a}^{6}\\right)}^{2}\\frac{1}{{m}^{3}{a}^{2}}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

17.\u00a0[latex]{\\left({b}^{-3}c\\right)}^{3}[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"149593\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"149593\"][latex]\\frac{{c}^{3}}{{b}^{9}}[\/latex][\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

18.\u00a0[latex]{\\left({x}^{2}{y}^{13}\u00f7{y}^{0}\\right)}^{2}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

19.\u00a0[latex]{\\left(9{z}^{3}\\right)}^{-2}y[\/latex]<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"623206\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"623206\"][latex]\\frac{y}{81{z}^{6}}[\/latex][\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n \r\n

For the following exercises, express the decimal in scientific notation.<\/p>\r\n\r\n

\r\n
\r\n

20. 148,000,000<\/p>\r\n21.\u00a00.0000314<\/span>\r\n

\r\n

[reveal-answer q=\"539160\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"539160\"][latex]3.14\u00d7{10}^{-5}[\/latex][\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

For the following exercises, convert each number in scientific notation to standard notation.<\/p>\r\n\r\n

\r\n
\r\n

22. [latex]9.8\u00d7{10}^{-9}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

\r\n\r\n23. [latex]1.6\u00d7{10}^{10}[\/latex]\r\n
\r\n

[reveal-answer q=\"583799\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"583799\"]16,000,000,000[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n

\r\n
\r\n

<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

\r\n

Real-World Applications<\/h4>\r\n
\r\n
\r\n

24. To reach escape velocity, a rocket must travel at the rate of [latex]2.2\u00d7{10}^{6}[\/latex] ft\/min. Rewrite the rate in standard notation.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

25. A dime is the thinnest coin in U.S. currency. A dime\u2019s thickness measures [latex]1.35\u00d7{10}^{-3}[\/latex] m. Rewrite the number in standard notation.<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"129465\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"129465\"]0.00135 m[\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

26. The average distance between Earth and the Sun is 92,960,000 mi. Rewrite the distance using scientific notation.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

27. A terabyte is made of approximately 1,099,500,000,000 bytes. Rewrite in scientific notation.<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"474120\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"474120\"][latex]1.0995\u00d7{10}^{12}[\/latex][\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

28. The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was [latex]\\$1.71496\u00d7{10}^{13}.[\/latex] Rewrite the GDP in standard notation.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

29. One picometer is approximately [latex]3.397\u00d7{10}^{-11}[\/latex] in. Rewrite this length using standard notation.<\/p>\r\n\r\n<\/div>\r\n

\r\n

[reveal-answer q=\"570406\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"570406\"]0.00000000003397 in.[\/hidden-answer]<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n
\r\n

30. The 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>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"

\n

PROBLEM SET<\/h3>\n
\n

For the following exercises, simplify the given expression. Write answers with positive exponents.<\/p>\n

\n
\n

1. [latex]\\frac{{a}^{3}{a}^{2}}{a}[\/latex]<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]{a}^{4}[\/latex]<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

2. [latex]\\frac{m{n}^{2}}{{m}^{-2}}[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n
\n

3.\u00a0[latex]{\\left({b}^{3}{c}^{4}\\right)}^{2}[\/latex]<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]{b}^{6}{c}^{8}[\/latex]<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

4.\u00a0[latex]{\\left(\\frac{{x}^{-3}}{{y}^{2}}\\right)}^{-5}[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n
\n

5.\u00a0[latex]a{b}^{2}\u00f7{d}^{-3}[\/latex]<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]a{b}^{2}{d}^{3}[\/latex]<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

6.\u00a0[latex]{\\left({w}^{0}{x}^{5}\\right)}^{-1}[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n
\n

7.\u00a0[latex]\\frac{{m}^{4}}{{n}^{0}}[\/latex]<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]{m}^{4}[\/latex]<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

8.\u00a0[latex]{y}^{-4}{\\left({y}^{2}\\right)}^{2}[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n
\n

9.\u00a0[latex]\\frac{{p}^{-4}{q}^{2}}{{p}^{2}{q}^{-3}}[\/latex]<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]\\frac{{q}^{5}}{{p}^{6}}[\/latex]<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

10.\u00a0[latex]{\\left(l \\cdot w \\right)}^{2}[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n
\n

11.\u00a0[latex]{\\left({y}^{7}\\right)}^{3}\u00f7{x}^{14}[\/latex]<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]\\frac{{y}^{21}}{{x}^{14}}[\/latex]<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

12.\u00a0[latex]{\\left(\\frac{a}{{2}^{3}}\\right)}^{2}[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n
\n

13.\u00a0[latex]{5}^{2}m\u00f7{5}^{0}m[\/latex]<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
25<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

14.\u00a0[latex]\\frac{{\\left(16\\sqrt{x}\\right)}^{2}}{{y}^{-1}}[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n
\n

15.\u00a0[latex]\\frac{{2}^{3}}{{\\left(3a\\right)}^{-2}}[\/latex]<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]72{a}^{2}[\/latex]<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

16.\u00a0[latex]{\\left(m{a}^{6}\\right)}^{2}\\frac{1}{{m}^{3}{a}^{2}}[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n
\n

17.\u00a0[latex]{\\left({b}^{-3}c\\right)}^{3}[\/latex]<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]\\frac{{c}^{3}}{{b}^{9}}[\/latex]<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

18.\u00a0[latex]{\\left({x}^{2}{y}^{13}\u00f7{y}^{0}\\right)}^{2}[\/latex]<\/p>\n<\/div>\n<\/div>\n

\n
\n

19.\u00a0[latex]{\\left(9{z}^{3}\\right)}^{-2}y[\/latex]<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]\\frac{y}{81{z}^{6}}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/div>\n

 <\/p>\n

For the following exercises, express the decimal in scientific notation.<\/p>\n

\n
\n

20. 148,000,000<\/p>\n

21.\u00a00.0000314<\/span><\/p>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]3.14\u00d7{10}^{-5}[\/latex]<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n<\/div>\n

For the following exercises, convert each number in scientific notation to standard notation.<\/p>\n

\n
\n

22. [latex]9.8\u00d7{10}^{-9}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n

23. [latex]1.6\u00d7{10}^{10}[\/latex]<\/p>\n

\n

\n

Show Answer<\/span><\/p>\n
16,000,000,000<\/div>\n<\/div>\n<\/div>\n
\n
\n

\n<\/div>\n<\/div>\n<\/div>\n

\n

Real-World Applications<\/h4>\n
\n
\n

24. To reach escape velocity, a rocket must travel at the rate of [latex]2.2\u00d7{10}^{6}[\/latex] ft\/min. Rewrite the rate in standard notation.<\/p>\n<\/div>\n<\/div>\n

\n
\n

25. A dime is the thinnest coin in U.S. currency. A dime\u2019s thickness measures [latex]1.35\u00d7{10}^{-3}[\/latex] m. Rewrite the number in standard notation.<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
0.00135 m<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

26. The average distance between Earth and the Sun is 92,960,000 mi. Rewrite the distance using scientific notation.<\/p>\n<\/div>\n<\/div>\n

\n
\n

27. A terabyte is made of approximately 1,099,500,000,000 bytes. Rewrite in scientific notation.<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
[latex]1.0995\u00d7{10}^{12}[\/latex]<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

28. The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was [latex]\\$1.71496\u00d7{10}^{13}.[\/latex] Rewrite the GDP in standard notation.<\/p>\n<\/div>\n<\/div>\n

\n
\n

29. One picometer is approximately [latex]3.397\u00d7{10}^{-11}[\/latex] in. Rewrite this length using standard notation.<\/p>\n<\/div>\n

\n

\n

Show Answer<\/span><\/p>\n
0.00000000003397 in.<\/div>\n<\/div>\n

 <\/p>\n<\/div>\n<\/div>\n

\n
\n

30. The 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<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":473810,"menu_order":8,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["jay-abramson"],"pb_section_license":"cc-by"},"chapter-type":[],"contributor":[75],"license":[57],"class_list":["post-15814","chapter","type-chapter","status-publish","hentry","contributor-jay-abramson","license-cc-by"],"part":15430,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15814","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/users\/473810"}],"version-history":[{"count":9,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15814\/revisions"}],"predecessor-version":[{"id":16730,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15814\/revisions\/16730"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/parts\/15430"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15814\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/media?parent=15814"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapter-type?post=15814"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/contributor?post=15814"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/license?post=15814"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}