4-2 Negative Exponents - Weebly

[Pages:16]4-2 Negative Exponents

Write each expression using a positive exponent. 1. SOLUTION:

= ANSWER:

2. SOLUTION: = ANSWER:

3. SOLUTION: = ANSWER:

4. SOLUTION: = ANSWER:

Write each fraction as an expression using a negative exponent other than -1. 5. SOLUTION:

=

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ANSWER:

ANSWER:

Write each fraction as an expression using a negative exponent other than -1. 5. SOLUTION:

= ANSWER:

6. SOLUTION: = ANSWER:

7. SOLUTION:

ANSWER:

8. SOLUTION:

ANSWER:

9. When a baseball is hit, it comes in contact with the bat for less than 0.001 of a second. Write 0.001 using a negative exponent other than ?1. SOLUTION:

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4-2ANNSWegERa:tive Exponents

9. When a baseball is hit, it comes in contact with the bat for less than 0.001 of a second. Write 0.001 using a negative exponent other than ?1. SOLUTION:

ANSWER:

12. SOLUTION:

ANSWER:

Evaluate each expression if x = -4 and y = 2. 10.

SOLUTION:

ANSWER:

13. SOLUTION:

ANSWER: 11.

SOLUTION:

ANSWER: 12.

SOLUTION:

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ANSWER:

Write each expression using a positive exponent. 14. SOLUTION:

=

ANSWER:

15. SOLUTION:

ANSWER:

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ANSWER:

4-2 Negative Exponents

15. SOLUTION:

ANSWER:

16. SOLUTION: = ANSWER:

17. SOLUTION: = ANSWER:

18. SOLUTION: = ANSWER:

19. SOLUTION: = ANSWER:

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ANSWER:

19. SOLUTION: =

ANSWER:

20. SOLUTION: =

ANSWER:

21. SOLUTION: = ANSWER:

Write each fraction as an expression using a negative exponent other than -1. 22. SOLUTION:

= ANSWER:

23. SOLUTION: = ANSWER:

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= ANSWER:

4-2 Negative Exponents

23. SOLUTION: = ANSWER:

24. SOLUTION: = ANSWER:

25. SOLUTION: = ANSWER:

26. SOLUTION:

ANSWER:

27. SOLUTION:

ANSWER:

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28.

ANSWER:

27. SOLUTION:

ANSWER:

28. SOLUTION:

ANSWER:

29. SOLUTION:

ANSWER: Write each decimal using a negative exponent. 30. The minimum thickness of Saturn's A ring is onetenth kilometer. SOLUTION:

ANSWER:

31. The diameter of a typical atom is 0.00000001 centimeter. Write the decimal using a negative exponent. SOLUTION:

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ANSWER:

4-2 Negative Exponents

31. The diameter of a typical atom is 0.00000001 centimeter. Write the decimal using a negative exponent.

SOLUTION:

ANSWER:

34. SOLUTION:

ANSWER:

Evaluate each expression if n = 3, p = -2, and q = 6. 32. SOLUTION:

ANSWER:

35. SOLUTION:

ANSWER: 33.

SOLUTION:

ANSWER: 34.

SOLUTION:

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ANSWER: 36.

SOLUTION:

ANSWER: 37.

SOLUTION:

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ANSWER:

4-2 Negative Exponents

37. SOLUTION:

ANSWER:

39. SOLUTION:

ANSWER: 38.

SOLUTION:

ANSWER: 39.

SOLUTION:

ANSWER:

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ANSWER:

40. SOLUTION:

ANSWER:

41. The table below shows the average lengths of different objects.

a. How many times as long is a virus than an atom?

b. About how many viruses would fit across a pinhead? c. A football field is about 102 meters long. How many times as long is this than a cell?

SOLUTION:

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a. To find how many times longer a virus is than an atom, divide the length of a virus by the length of an

a. How many times as long is a virus than an atom? b. About how many viruses would fit across a pinhead?

4-2c.NAefogotabatlilvfieeldEisxabpouot n10e2nmtesters long. How many times as long is this than a cell?

SOLUTION:

a. To find how many times longer a virus is than an atom, divide the length of a virus by the length of an atom.

42. The pH of a substance is a measure of its acidity. The pH scale ranges from 0 to 14, with a pH of 7 being neutral. As the pH decreases, the substance is more acidic. The table shows the pH of several common substances.

So, a virus is 103 or 1000 times as long as an atom. b. To find how many viruses would fit across a pinhead, divide the length of a pinhead by the length of a virus.

So, 104 or 10,000 viruses would fit across a pinhead. c. To find how many times as long a football field is than a cell, divide the length of a football field by the length of a cell.

a. Which substance in the table has the greatest hydrogen ion concentration? How many times as great is that hydrogen ion concentration than that of egg whites? b. Which substance has a hydrogen ion concentration of one millionth? c. How many times as great is the hydrogen ion concentration of coffee as the hydrogen ion concentration of pure water?

SOLUTION:

a. Since is the largest value in the hydrogen ion concentration column, coffee has the greatest hydrogen ion concentration. To find how many times as great the hydrogen ion concentration of coffee is than that of egg whites, divide the concentration for coffee by the concentration for egg whites.

So, a football field is 106 or 1,000,000 times as long as a cell.

ANSWER: a. 103 or 1000 times b. 104 or 10,000 c. 106 or 1,000,000 times

42. The pH of a substance is a measure of its acidity. The pH scale ranges from 0 to 14, with a pH of 7 being neutral. As the pH decreases, the substance is more acidic. The table shows the pH of several common substances.

So, the hydrogen ion concentration of coffee is 103 or 1000 times as great as that of egg whites. b. One million = 1,000,000 or 106, so one millionth =

or 10-6. Milk has a hydrogen ion

concentration of 10-6 or one millionth.

c. To find how many times as great the hydrogen ion concentration of coffee is than that of pure water, divide the concentration for coffee by the concentration for pure water.

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a. Which substance in the table has the greatest

So, the hydrogen ion concentration of coffee is 1P0a2goer7 100 times as great as that of pure water.

ANSWER:

4-2 Negative Exponents

So, the hydrogen ion concentration of coffee is 102 or 100 times as great as that of pure water.

ANSWER: a. coffee, 103 or 1000 times b. milk c. 102 or 100 times

43. Be Precise A grain of sand has a volume of about cubic millimeter.

a. Write this number using a negative exponent. b. An empty bottle used to create sand art can hold about 1010 grains of sand. What is the approximate volume of the sand art bottle? c. If one cubic centimeter is equal to 103 cubic millimeters, how many cubic centimeters of sand will the bottle hold? SOLUTION: a.

b. To find the approximate volume of the sand art bottle, multiply the number of grains of sand the bottle can hold by the volume of one grain of sand.

So, the approximate volume of the sand art bottle is 106 mm3. c. To find how many cubic centimeters of sand the bottle will hold, divide the volume of the bottle by the number of cubic millimeters in one cubic centimeter.

The bottle will hold 103 or 1000 cm3 of sand.

ANSWER: a. 10-4 b. 106 mm3 c. 103 cm3

44. The wavelength of X-rays are between 1 and 10 nanometers. If a nanometer is equal to a billionth of a

eSolutmionesteMra, neuxapl r- ePsoswtehreedgbryeCaotegsnterwo avelength of an X-ray in meters. Write the expression using a negative exponent.

ANSWER: a. 10-4 b. 106 mm3 c. 103 cm3

44. The wavelength of X-rays are between 1 and 10 nanometers. If a nanometer is equal to a billionth of a meter, express the greatest wavelength of an X-ray in meters. Write the expression using a negative exponent.

SOLUTION:

1 nanometer =

meter

To express the greatest wavelength of an X-ray in meters, multiply the greatest wavelength in nanometers by the number of meters in 1 nanometer.

The greatest wavelength of an X-ray is 10-8 meters.

ANSWER: 10-8 m

45. The shortest period of time ever measured directly was a light burst of a laser lasting about 0.000000000000001 second. Write this decimal as a fraction and as a power of ten.

SOLUTION:

ANSWER:

; 10-15

46. Multiple Representations In this problem, you will explore negative exponents when using powers of 10,

10-1 = or 0.1.

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