Problem Set: Exponents and Scientific Notation

PROBLEM SET

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

1. a3a2a

 

2. mn2m2

3. (b3c4)2

 

4. (x3y2)5

5. ab2÷d3

 

6. (w0x5)1

7. m4n0

 

8. y4(y2)2

9. p4q2p2q3

 

10. (lw)2

11. (y7)3÷x14

 

12. (a23)2

13. 52m÷50m

 

14. (16x)2y1

15. 23(3a)2

 

16. (ma6)21m3a2

17. (b3c)3

 

18. (x2y13÷y0)2

19. (9z3)2y

 

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. 9.8×109

23. 1.6×1010

Real-World Applications

24. To reach escape velocity, a rocket must travel at the rate of 2.2×106 ft/min. Rewrite the rate in standard notation.

25. A dime is the thinnest coin in U.S. currency. A dime’s thickness measures 1.35×103 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 $1.71496×1013. Rewrite the GDP in standard notation.

29. One picometer is approximately 3.397×1011 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.