PROBLEM SET
For the following exercises, simplify the given expression. Write answers with positive exponents.
1. a3a2a
2. mn2m−2
3. (b3c4)2
4. (x−3y2)−5
5. ab2÷d−3
6. (w0x5)−1
7. m4n0
8. y−4(y2)2
9. p−4q2p2q−3
10. (l⋅w)2
11. (y7)3÷x14
12. (a23)2
13. 52m÷50m
14. (16√x)2y−1
15. 23(3a)−2
16. (ma6)21m3a2
17. (b−3c)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. 9.8×10−9
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 1.35×10−3 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 3.397×10−11 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.