Problem Set: Exponents and Scientific Notation

PROBLEM SET

For the following exercises, simplify the given expression. Write answers with positive exponents.

1. [latex]\frac{{a}^{3}{a}^{2}}{a}[/latex]

 

2. [latex]\frac{m{n}^{2}}{{m}^{-2}}[/latex]

3. [latex]{\left({b}^{3}{c}^{4}\right)}^{2}[/latex]

 

4. [latex]{\left(\frac{{x}^{-3}}{{y}^{2}}\right)}^{-5}[/latex]

5. [latex]a{b}^{2}÷{d}^{-3}[/latex]

 

6. [latex]{\left({w}^{0}{x}^{5}\right)}^{-1}[/latex]

7. [latex]\frac{{m}^{4}}{{n}^{0}}[/latex]

 

8. [latex]{y}^{-4}{\left({y}^{2}\right)}^{2}[/latex]

9. [latex]\frac{{p}^{-4}{q}^{2}}{{p}^{2}{q}^{-3}}[/latex]

 

10. [latex]{\left(l \cdot w \right)}^{2}[/latex]

11. [latex]{\left({y}^{7}\right)}^{3}÷{x}^{14}[/latex]

 

12. [latex]{\left(\frac{a}{{2}^{3}}\right)}^{2}[/latex]

13. [latex]{5}^{2}m÷{5}^{0}m[/latex]

 

14. [latex]\frac{{\left(16\sqrt{x}\right)}^{2}}{{y}^{-1}}[/latex]

15. [latex]\frac{{2}^{3}}{{\left(3a\right)}^{-2}}[/latex]

 

16. [latex]{\left(m{a}^{6}\right)}^{2}\frac{1}{{m}^{3}{a}^{2}}[/latex]

17. [latex]{\left({b}^{-3}c\right)}^{3}[/latex]

 

18. [latex]{\left({x}^{2}{y}^{13}÷{y}^{0}\right)}^{2}[/latex]

19. [latex]{\left(9{z}^{3}\right)}^{-2}y[/latex]

 

For the following exercises, express the decimal in scientific notation.

20. 148,000,000

21. 0.0000314

 

For the following exercises, convert each number in scientific notation to standard notation.

22. [latex]9.8×{10}^{-9}[/latex]

23. [latex]1.6×{10}^{10}[/latex]

Real-World Applications

24. To reach escape velocity, a rocket must travel at the rate of [latex]2.2×{10}^{6}[/latex] ft/min. Rewrite the rate in standard notation.

25. A dime is the thinnest coin in U.S. currency. A dime’s thickness measures [latex]1.35×{10}^{-3}[/latex] m. Rewrite the number in standard notation.

 

26. The average distance between Earth and the Sun is 92,960,000 mi. Rewrite the distance using scientific notation.

27. A terabyte is made of approximately 1,099,500,000,000 bytes. Rewrite in scientific notation.

 

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

29. One picometer is approximately [latex]3.397×{10}^{-11}[/latex] in. Rewrite this length using standard notation.

 

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.