U.S. Population In June 2010, the population of the United

In the expression 23 , the 3 is known as the .

In the expression 23 , the 2 is known as the .

The product x # x # x # x # x can also be written as the exponential expression .

With the product rule for exponents, the expression x2 # x3 can be simplified to .

With the quotient rule for exponents, the expression x7 x4 can be simplified to .

With the zero exponent rule, the expression 70 can be simplified to .

With the negative exponent rule, for x 0, the expression x-5 can be simplified to .

With the power rule for exponents, the expression (x2 ) 3 can be simplified to .

When written in scientific notation, the number 2013 is .

When written in scientific notation, the number 0.0034 is .

When written in decimal notation, the number \(5.73 \times 10^{-5}\) is __________.

When written in decimal notation, the number 1.776 * 103 is .

In Exercises 13 40, evaluate the expression. Assume x 0.a) 32 b) 23

In Exercises 13 40, evaluate the expression. Assume x 0.a) 25 b) 52

In Exercises 13 40, evaluate the expression. Assume x 0.a) (-5)2 b) -52

In Exercises 13 40, evaluate the expression. Assume x 0.a) -32 b) (-3)2

In Exercises 13– 40, evaluate the expression. Assume \(x \neq 0\). \(\text { a) }-2^{4}\) \(\text { b) }(-2)^{4}\)

In Exercises 13 40, evaluate the expression. Assume x 0.a) (-3)4 b) -34

In Exercises 13 40, evaluate the expression. Assume x 0.a) -43 b) (-4)3

In Exercises 13 40, evaluate the expression. Assume x 0.a) (-2)7 b) -27

In Exercises 13-40, evaluate the expression. Assume x \(\neq\) 0. a) \(-\left(\frac{1}{2}\right)^{2}\) b) \(\left(-\frac{1}{2}\right)^{2}\)

In Exercises 13 40, evaluate the expression. Assume x 0.a) - a 1 2 b 3 b) a-1 2 b 3

In Exercises 13 40, evaluate the expression. Assume x 0.a) 1001 b) 1100

In Exercises 13 40, evaluate the expression. Assume x 0.a) 20121 b) 12012

In Exercises 13 40, evaluate the expression. Assume x 0.a) 32 # 33 b) (-3)2 # (-3)3

In Exercises 13 40, evaluate the expression. Assume x 0.a) 23 # 2 b) (-2)3 # (-2)

In Exercises 13 40, evaluate the expression. Assume x 0.a) 57 55 b) (-5)7 (-5)5

In Exercises 13 40, evaluate the expression. Assume x 0.a) 45 42 b) (-4)5 (-4)2

In Exercises 13 40, evaluate the expression. Assume x 0.a) 60 b) -60

In Exercises 13 40, evaluate the expression. Assume x 0.a) (-6)0 b) -(-6)0

In Exercises 13– 40, evaluate the expression. Assume \(x \neq 0\). a) \(6^0\) b) \(-6^0\)

In Exercises 13 40, evaluate the expression. Assume x 0.a) -6x0 b) (-6x) 0

In Exercises 13 40, evaluate the expression. Assume x 0.a) 3-3 b) 7-2

In Exercises 13 40, evaluate the expression. Assume x 0.a) 5-1 b) 2-4

In Exercises 13 40, evaluate the expression. Assume x 0.a) -9-2 b) (-9)-2

In Exercises 13 40, evaluate the expression. Assume x 0.a) -5-2 b) (-5)-2

In Exercises 13 40, evaluate the expression. Assume x 0.a) (22 ) 3 b) (23 ) 2

In Exercises 13 40, evaluate the expression. Assume x 0.a) c a 1 2 b 2 d 3 b) c a -1 2 b 2 d 3

In Exercises 13 40, evaluate the expression. Assume x 0.a) 43 # 4-2 b) 2-2 # 2-2

In Exercises 13 40, evaluate the expression. Assume x 0.a) (-5)-2 (-5)-2 b) (-1)-5 (-1)-5

In Exercises 4152, express the number in scientific notation.415000

In Exercises 4152, express the number in scientific notation.923000000

In Exercises 4152, express the number in scientific notation.0.00275

In Exercises 4152, express the number in scientific notation.0.000034

In Exercises 41–52, express the number in scientific notation. 0.56

In Exercises 4152, express the number in scientific notation.0.00467

In Exercises 41–52, express the number in scientific notation. 19,000

In Exercises 4152, express the number in scientific notation.1260000000

In Exercises 4152, express the number in scientific notation.0.000186

In Exercises 4152, express the number in scientific notation.0.0003

In Exercises 4152, express the number in scientific notation.0.00000423

In Exercises 4152, express the number in scientific notation.54000

In Exercises 5362, express the number in decimal notation. 4.2 * 104

In Exercises 5362, express the number in decimal notation. 3.9 * 105

In Exercises 53-62, express the number in decimal notation. 1.32 X 10-2

In Exercises 5362, express the number in decimal notation. 4.003 * 107

In Exercises 5362, express the number in decimal notation. 8.62 * 10-5

In Exercises 5362, express the number in decimal notation. 2.19 * 10-4

In Exercises 5362, express the number in decimal notation. 3.12 * 10-1

In Exercises 5362, express the number in decimal notation. 4.6 * 101

In Exercises 5362, express the number in decimal notation. 9 * 106

In Exercises 5362, express the number in decimal notation. 7.3 * 104

In Exercises 6372, (a) perform the indicated operation without the use of a calculator and express each answer in decimal notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in scientific notation, convert the answer to decimal notation.(2 * 103 )(3.1 * 102

In Exercises 6372, (a) perform the indicated operation without the use of a calculator and express each answer in decimal notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in scientific notation, convert the answer to decimal notation.(4.9 * 104 )(2 * 103 )

In Exercises 6372, (a) perform the indicated operation without the use of a calculator and express each answer in decimal notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in scientific notation, convert the answer to decimal notation.(5.1 * 101 )(3 * 10-4 )

In Exercises 6372, (a) perform the indicated operation without the use of a calculator and express each answer in decimal notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in scientific notation, convert the answer to decimal notation.(1.6 * 10-2 )(4 * 10-3 )

In Exercises 6372, (a) perform the indicated operation without the use of a calculator and express each answer in decimal notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in scientific notation, convert the answer to decimal notation.7.5 * 106 3 * 104

In Exercises 6372, (a) perform the indicated operation without the use of a calculator and express each answer in decimal notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in scientific notation, convert the answer to decimal notation.5.2 * 107 4 * 109

In Exercises 6372, (a) perform the indicated operation without the use of a calculator and express each answer in decimal notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in scientific notation, convert the answer to decimal notation.8.4 * 10-6 4 * 10-3

In Exercises 6372, (a) perform the indicated operation without the use of a calculator and express each answer in decimal notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in scientific notation, convert the answer to decimal notation.25 * 103 5 * 10-2

In Exercises 6372, (a) perform the indicated operation without the use of a calculator and express each answer in decimal notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in scientific notation, convert the answer to decimal notation.4 * 105 2 * 104

In Exercises 6372, (a) perform the indicated operation without the use of a calculator and express each answer in decimal notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in scientific notation, convert the answer to decimal notation.16 * 103 8 * 10-3

In Exercises 73-82, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation. (1,000,000)(230,000)

In Exercises 73 82, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation.(2,000,000)(0.00025)

In Exercises 73 82, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation.(0.003)(0.00015)

In Exercises 73 82, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation.(230,000)(3000)

In Exercises 73 82, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation.5,600,000 80,000

In Exercises 73 82, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation.28,000 0.004

In Exercises 73 82, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation.0.00004 200

In Exercises 73 82, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation.0.0012 0.000006

In Exercises 73 82, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation.150,000 0.0005

In Exercises 73 – 82, (a) perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in decimal notation, convert the answer to scientific notation. \(\frac{24,000}{8,000,000}\)

In Exercises 8386, list the numbers from smallest to largest. 1.03 * 104 ; 1.7; 3.6 * 10-3 ; 9.8 * 102

In Exercises 8386, list the numbers from smallest to largest.8.5 * 10-5 ; 8.2 * 103 ; 1.3 * 10-1 ; 6.2 * 104

In Exercises 8386, list the numbers from smallest to largest.40,000; 4.1 * 103 ; 0.00079; 8.3 * 10-5

In Exercises 8386, list the numbers from smallest to largest.267,000,000; 3.14 * 107 ; 1,962,000; 4.79 * 106

U.S. Debt per Person: 2006 Versus 2010 In Example 14 on page 265, the U.S. government debt was discussed. It was found that the debt in 2010 was about $42,261.71 per person. In 2006, the U.S. government debt was about $8.38 trillion, and the population of the United States was about 299 million. a) Determine the amount of debt per person in 2006. b) How much more per person did the U.S. government owe in 2010 than in 2006?

United Kingdom Debt per Person In 2010, the United Kingdoms government had a debt of about 923 billion (the pound, symbolized, , is the United Kingdoms unit of currency). The United Kingdoms population in 2010 was about 62.8 million. a) Determine the amount of debt per person in 2010 for the United Kingdom. b) In 2010, 1 was worth about $1.50. Convert the amount found in part (a) to dollars.

U.S. Population In June 2010, the population of the United States was about 309.5 million people, and the population of the world was about 6.830 billion people. Determine the ratio of the U.S. population to the worlds population by dividing the U.S. population by the worlds population. Write your answer as a decimal number and round to the nearest thousandth.

Chinas Population In June 2010, the population of China was about 1.319 billion people, and the population of the world was about 6.830 billion people. Determine the ratio of Chinas population to the worlds population by dividing Chinas population by the worlds population. Write your answer as a decimal number and round to the nearest thousandth

New York Population Density In June 2010, the population of the metropolitan New York area was about 17,800,000 people, and the area was about 8683 square kilometers. Determine the metropolitan New York population density by dividing the population by the area

Mumbai Population Density In June 2010, the population of the metropolitan Mumbai, India, area was about 14,350,000 people, and the area was about 484 square kilometers. Determine the metropolitan Mumbai population density by dividing the population by the area.

Gross Domestic Product The gross domestic product (GDP) of a country is the total national output of goods and services produced within that country. In 2009, the GDP of the United States was about $14.3 trillion, and the U.S. population was about 308 million people. Determine the U.S. GDP per person by dividing the GDP by the population. Round your answer to the nearest whole dollar.

Chinas GDP In 2009, the GDP (see Exercise 93) of China was about $4.91 trillion, and the population of China was about 1.335 billion people. Determine Chinas GDP per person by dividing the GDP by the population. Round your answer to the nearest whole dollar.

Traveling to the Moon The distance from Earth to the moon is approximately 239,000 mi. If a spacecraft travels at a speed of 20,000 mph, how many hours would the spacecraft need to travel from Earth to the moon? Use distance = rate * time.

Traveling to Jupiter The distance from Earth to the planet Jupiter is approximately 4.5 * 108 mi. If a spacecraft traveled at a speed of 25,000 mph, how many hours would the spacecraft need to travel from Earth to Jupiter? Use distance = rate * time.

Traveling to Proxima Centauri The star closest in distance to our own sun is Proxima Centauri. The distance from Earth to Proxima Centauri is approximately 2.5 * 1013 miles. If a spacecraft travels at a speed of 20,000 mph, how many hours would the spacecraft need to travel to Proxima Centauri? Use distance  rate  time and write your answer in scientific notation

Computer Speed As of June 22, 2010, the fastest computer in the world was the Cray Jaguar located at Oak Ridge National Laboratory. This computer is capable of performing about 1.75 quadrillion (1.75 * 1015) calculations per second. At this rate, how long would it take to perform a task requiring 7.6 * 1065 calculations? Write your answer in scientific notation.

1950 Niagara Treaty The 1950 Niagara Treaty between the United States and Canada requires that during the tourist season a minimum of 100,000 cubic feet of water per second (ft3 /sec) flow over Niagara Falls (another 130,0009160,000 ft3 /sec are diverted for power generation). Find the minimum amount of water that will flow over the falls in a 24-hour period during the tourist season. Write your answer in scientific notation.

Bucket Full of Molecules A drop of water contains about 40 billion molecules. If a bucket has half a million drops of water in it, how many molecules of water are in the bucket? Write your answer in scientific notation.

Blood Cells in a Cubic Millimeter If a cubic millimeter of blood contains 5,800,000 red blood cells, how many red blood cells are contained in 50 cubic millimeters of blood? Write your answer in scientific notation.

Radioactive Isotopes The half-life of a radioactive isotope is the time required for half the quantity of the isotope to decompose. The half-life of uranium-238 is 4.5 * 109 years, and the half-life of uranium-234 is 2.5 * 105 years. How many times greater is the half-life of uranium-238 than uranium-234?

Mutual Fund Manager Lauri Mackey is the fund manager for the Mackey Mutual Fund. This mutual fund has total assets of $1.2 billion. Lauri wants to maintain the investments in this fund according to the following pie chart. U.S. stocks 60% International stocks 10% Government bonds 25% Cash 5% a) How much of the $1.2 billion should be invested in U.S. stocks? b) How much should be invested in government bonds? c) How much should be invested in international stocks? d) How much should remain in cash?

Another Mutual Fund Manager Susan Dratch is the fund manager for the Dratch Mutual Fund. This mutual fund has total assets of $3.4 billion. Susan wants to maintain the investments in this fund according to the following pie chart. Government bonds 40% U.S. stocks 40% International stocks 10% Cash 10% a) How much of the $3.4 billion should be invested in U.S. stocks? b) How much should be invested in government bonds? c) How much should be invested in international stocks? d) How much should remain in cash?

Metric System Comparison In the metric system, 1 meter = 103 millimeters. How many times greater is a meter than a millimeter?

Milligrams and Kilograms In the metric system, 1 gram = 103 milligrams and 1 gram = 10-3 kilogram. What is the relationship between milligrams and kilograms?

Earth to Sun Comparison The mass of the sun is approximately \(2 \times 10^{30}\) 0 kilograms, and the mass of Earth is approximately \(6 \times 10^{24}\) kilograms. How many times greater is the mass of the sun than the mass of Earth? Write your answer in decimal notation.

Comparing a Million to a Billion Many people have no idea of the difference in size between a million (1,000,000), a billion (1,000,000,000), and a trillion (1,000,000,000,000). a) Write a million, a billion, and a trillion in scientific notation. b) Determine how long it would take to spend one million dollars if you spent $1000 a day. c) Repeat part (b) for one billion dollars. d) Repeat part (b) for one trillion dollars. e) How many times greater is one billion dollars than one million dollars?

Speed of Light a) Light travels at a speed of 1.86 * 105 mi/sec. A lightyear is the distance that light travels in 1 year. Determine the number of miles in a light-year. b) Earth is approximately 93,000,000 mi from the sun. How long does it take light from the sun to reach Earth?

Bacteria in a Culture The exponential function E(t) = 210 # 2t approximates the number of bacteria in a certain culture after t hours. a) The initial number of bacteria is determined when t = 0. What is the initial number of bacteria? b) How many bacteria are there after 1 2 hour?

Obtain data from the U.S. Department of the Treasury and from the U.S. Bureau of the Census Internet Web sites to calculate the current U.S. government debt per person. Write a report in which you compare your figure with those obtained in Exercise 87 and Example 14. Include in your report definitions of the following terms: revenues, expenditures, deficit, and surplus.

John Allen Paulos Read the Profiles in Mathematics box on page 264. Read one of Pauloss books and write a 500-word report on it.

Find an article in a newspaper or magazine that contains scientific notation. Write a paragraph explaining how scientific notation was used. Attach a copy of the article to your report