The bar graph shows the total amount Americans paid in federaltaxes, in trillions of

Fill in each blank so that the resulting statement is true. The product rule for exponents states that bm # bn = . When multiplying exponential expressions with the same base, the exponents.

Fill in each blank so that the resulting statement is true. The quotient rule for exponents states that bm bn = , b 0. When dividing exponential expressions with the same nonzero base, the exponents.

Fill in each blank so that the resulting statement is true. If b 0, then b0 = .

Fill in each blank so that the resulting statement is true. The negative-exponent rule states that b-n = , b 0.

Fill in each blank so that the resulting statement is true. True or false: 5-2 = -52

Fill in each blank so that the resulting statement is true. Negative exponents in denominators can be evaluated using 1 b-n = , b 0.

Fill in each blank so that the resulting statement is true. True or false: 1 8-2 = 82

Fill in each blank so that the resulting statement is true. A positive number is written in scientific notation when it is expressed in the form a * 10n, where a is and n is a/an .

Fill in each blank so that the resulting statement is true. True or false: 4 * 103 is written in scientific notation.

Fill in each blank so that the resulting statement is true. True or false: 40 * 102 is written in scientific notation.

Evaluate each exponential expression in Exercises 122. 4-3

Evaluate each exponential expression in Exercises 122. 2-6

Evaluate each exponential expression in Exercises 1–22. 13.) \(2^{2} \cdot 2^{3}\)

Evaluate each exponential expression in Exercises 122. 33 # 32

Evaluate each exponential expression in Exercises 122. (22 ) 3

Evaluate each exponential expression in Exercises 122. (33 ) 2

Evaluate each exponential expression in Exercises 122. 28 24

Evaluate each exponential expression in Exercises 122. 38 34

Evaluate each exponential expression in Exercises 122. 3-3 # 3

Evaluate each exponential expression in Exercises 122. 2-3 # 2

Evaluate each exponential expression in Exercises 122. 23 27

Evaluate each exponential expression in Exercises 122. 34 37

Simplify each exponential expression in Exercises 2364. x-2y

Simplify each exponential expression in Exercises 2364. xy-3

Simplify each exponential expression in Exercises 2364. x0y5

Simplify each exponential expression in Exercises 2364. x7y0

Simplify each exponential expression in Exercises 2364. x3 # x7

Simplify each exponential expression in Exercises 2364. x11 # x5

Simplify each exponential expression in Exercises 2364. x-5 # x10

Simplify each exponential expression in Exercises 2364. x-6 # x12

Simplify each exponential expression in Exercises 2364. (x3 ) 7

Simplify each exponential expression in Exercises 2364. (x11 ) 5

Simplify each exponential expression in Exercises 2364. (x-5 ) 3

Simplify each exponential expression in Exercises 2364. (x-6 ) 4

Simplify each exponential expression in Exercises 2364. x14 x7

Simplify each exponential expression in Exercises 2364. x30 x10

Simplify each exponential expression in Exercises 2364. x14 x-7

Simplify each exponential expression in Exercises 2364. x30 x-10

Simplify each exponential expression in Exercises 2364. (8x3 ) 2

Simplify each exponential expression in Exercises 2364. (6x4 ) 2

Simplify each exponential expression in Exercises 2364. a - 4 x b 3

Simplify each exponential expression in Exercises 2364. a - 6 y b 3

Simplify each exponential expression in Exercises 2364. (-3x2y5 ) 2

Simplify each exponential expression in Exercises 2364. (-3x4y6 ) 3

Simplify each exponential expression in Exercises 2364. (3x4 )(2x7 )

Simplify each exponential expression in Exercises 2364. (11x5 )(9x12 )

Simplify each exponential expression in Exercises 2364. (-9x3y)(-2x6y4 )

Simplify each exponential expression in Exercises 2364. (-5x4y)(-6x7y11 )

Simplify each exponential expression in Exercises 2364. 8x20 2x4

Simplify each exponential expression in Exercises 2364. 20x24 10x6

Simplify each exponential expression in Exercises 2364. 25a13b4 -5a2b3

Simplify each exponential expression in Exercises 2364. 35a14b6 -7a7b3

Simplify each exponential expression in Exercises 2364. 14b7 7b14

Simplify each exponential expression in Exercises 2364. 20b10 10b20

Simplify each exponential expression in Exercises 2364. (4x3 ) -2

Simplify each exponential expression in Exercises 2364. 10x2 ) -3

Simplify each exponential expression in Exercises 2364. 24x3y5 32x7y-9

Simplify each exponential expression in Exercises 2364. 10x4y9 30x12y-3

Simplify each exponential expression in Exercises 2364. 5x3 y -2

Simplify each exponential expression in Exercises 2364. 3x4 y -3

Simplify each exponential expression in Exercises 2364. -15a4b2 5a10b-3 3

Simplify each exponential expression in Exercises 2364. -30a14b8 10a17b-2 3

Simplify each exponential expression in Exercises 2364. 3a-5b2 12a3b-4 0

Simplify each exponential expression in Exercises 2364. 4a-5b3 12a3b-5 0

In Exercises 6576, write each number in decimal notation without the use of exponents. 3.8 * 102

In Exercises 6576, write each number in decimal notation without the use of exponents. 9.2 * 102

In Exercises 6576, write each number in decimal notation without the use of exponents. 6 * 10-4

In Exercises 6576, write each number in decimal notation without the use of exponents. 7 * 10-5

In Exercises 6576, write each number in decimal notation without the use of exponents. -7.16 * 106

In Exercises 6576, write each number in decimal notation without the use of exponents. -8.17 * 106

In Exercises 6576, write each number in decimal notation without the use of exponents. 7.9 * 10-1

In Exercises 6576, write each number in decimal notation without the use of exponents. 6.8 * 10-1

In Exercises 6576, write each number in decimal notation without the use of exponents. 4.15 * 10-3

In Exercises 6576, write each number in decimal notation without the use of exponents. -3.14 * 10-3

In Exercises 6576, write each number in decimal notation without the use of exponents. 6.00001 * 1010

In Exercises 6576, write each number in decimal notation without the use of exponents. 7.00001 * 1010

In Exercises 7786, write each number in scientific notation. 32,000

In Exercises 7786, write each number in scientific notation. 64,000

In Exercises 7786, write each number in scientific notation. 638,000,000,000,000,000

In Exercises 7786, write each number in scientific notation. 579,000,000,000,000,000

In Exercises 7786, write each number in scientific notation. -5716

In Exercises 7786, write each number in scientific notation. -3829

In Exercises 7786, write each number in scientific notation. 0.0027

In Exercises 7786, write each number in scientific notation. 0.0083

In Exercises 7786, write each number in scientific notation. -0.00000000504

In Exercises 7786, write each number in scientific notation. -0.00000000405

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (3 * 104 )(2.1 * 103 )

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (2 * 104 )(4.1 * 103 )

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (1.6 * 1015 )(4 * 10-11 )

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (1.4 * 1015 )(3 * 10-11 )

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (6.1 * 10-8 )(2 * 10-4 )

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (5.1 * 10-8 )(3 * 10-4 )

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (4.3 * 108 )(6.2 * 104 )

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (8.2 * 108 )(4.6 * 104 )

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 8.4 * 108 4 * 105

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 6.9 * 108 3 * 105

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 3.6 * 104 9 * 10-2

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 1.2 * 104 2 * 10-2

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 4.8 * 10-2 2.4 * 106

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 7.5 * 10-2 2.5 * 106

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 2.4 * 10-2 4.8 * 10-6

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 1.5 * 10-2 3 * 10-6

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 480,000,000,000 0.00012

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 282,000,000,000 0.00141

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 0.00072 * 0.003 0.00024

In Exercises 87106, perform the indicated computations. Write theanswers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 66,000 * 0.001 0.003 * 0.002

In Exercises 107114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (x-2y) -3 (x2y-1 ) 3

In Exercises 107114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (xy-2 ) -2 (x-2y) -3

In Exercises 107114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (2x-3yz-6 )(2x) -5

In Exercises 107114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x-4yz-7 )(3x) -3

In Exercises 107114, simplify each exponential expression. Assume that variables represent nonzero real numbers. x3y4z5 x-3y-4z-5 -2

In Exercises 107114, simplify each exponential expression. Assume that variables represent nonzero real numbers. x4y5z6 x-4y-5z-6 -4

In Exercises 107114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (2-1x-2y-1 ) -2 (2x-4y3 ) -2 (16x-3y3 ) 0 (2x-3 y -5 ) 2

In Exercises 107114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (2-1x-3y-1 ) -2 (2x-6y4 ) -2 (9x3y-3 ) 0 (2x-4 y -6 ) 2

The bar graph shows the total amount Americans paid in federal taxes, in trillions of dollars, and the U.S. population, in millions, from 2012 through 2015. Exercises 115116 are based on the numbers displayed by the graph. a. In 2015, the United States government collected $3.18 trillion in taxes. Express this number in scientific notation. b. In 2015, the population of the United States was approximately 320 million. Express this number in scientific notation. c. Use your scientific notation answers from parts (a) and (b) to answer this question: If the total 2015 tax collections were evenly divided among all Americans, how much would each citizen pay? Express the answer indecimal notation, rounded to the nearest dollar.

The bar graph shows the total amount Americans paid in federal taxes, in trillions of dollars, and the U.S. population, in millions, from 2012 through 2015. Exercises 115116 are based on the numbers displayed by the graph. a. In 2014, the United States government collected $3.02 trillion in taxes. Express this number in scientific notation. b. In 2014, the population of the United States was approximately 319 million. Express this number in scientific notation. c. Use your scientific notation answers from parts (a) and (b) to answer this question: If the total 2014 tax collections were evenly divided among all Americans, how much would each citizen pay? Express the answer indecimal notation, rounded to the nearest dollar.

We have seen that the 2016 U.S. national debt was $18.9 trillion. In Exercises 117118, you will use scientific notation to put a number like 18.9 trillion in perspective. a. Express 18.9 trillion in scientific notation. b. Four years of tuition, fees, and room and board at a public U.S. college cost approximately $60,000. Express this number in scientific notation. c. Use your answers from parts (a) and (b) to determine how many Americans could receive a free college education for $18.9 trillion.

We have seen that the 2016 U.S. national debt was $18.9 trillion. In Exercises 117118, you will use scientific notation to put a number like 18.9 trillion in perspective. a. Express 18.9 trillion in scientific notation. b. Each year, Americans spend $254 billion on summer vacations. Express this number in scientific notation. c. Use your answers from parts (a) and (b) to determine how many years Americans can have free summer vacations for $18.9 trillion.

In 2012, the United States government spent more than it had collected in taxes, resulting in a budget deficit of $1.09trillion. a. Express 1.09 trillion in scientific notation. b. There are approximately 32,000,000 seconds in a year. Write this number in scienfic notation. c. Use your answers from parts (a) and (b) to determine approximately how many years is 1.09 trillion seconds. (Note: 1.09 trillion seconds would take us back in time to a period when Neanderthals were using stones to make tools.)

Refer to the Blitzer Bonus on page 32. Use scientific notation to verify any two of the bulleted items on ways to spend $1trillion.

Describe what it means to raise a number to a power. In your description, include a discussion of the difference between -52 and (-5) 2.

Explain the product rule for exponents. Use 23 # 25 in your explanation.

Explain the power rule for exponents. Use (32 ) 4 in your explanation.

Explain the quotient rule for exponents. Use 58 52 in your explanation.

Why is (-3x2 )(2x-5 ) not simplified? What must be done to simplify the expression?

How do you know if a number is written in scientific notation?

Explain how to convert from scientific to decimal notation and give an example.

Explain how to convert from decimal to scientific notation and give an example.

Make Sense? In Exercises 129132, determine whether each statement makes sense or does not make sense, and explain your reasoning. There are many exponential expressions that are equal to 36x12 , such as (6x6 ) 2 , (6x3 )(6x9 ), 36(x3 ) 9 , and 62 (x2 ) 6 .

Make Sense? In Exercises 129132, determine whether each statement makes sense or does not make sense, and explain your reasoning. If 5-2 is raised to the third power, the result is a number between 0 and 1.

Make Sense? In Exercises 129132, determine whether each statement makes sense or does not make sense, and explain your reasoning. The population of Colorado is approximately 4.6 * 1012 .

Make Sense? In Exercises 129132, determine whether each statement makes sense or does not make sense, and explain your reasoning. I just finished reading a book that contained approximately 1.04 * 105 words.

In Exercises 133140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 4-2 6 4-3

In Exercises 133140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 5-2 7 2-5

In Exercises 133140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. (-2) 4 = 2-4

In Exercises 133140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 52 # 5-2 7 25 # 2-5

In Exercises 133140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 534.7 = 5.347 * 103

In Exercises 133140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 8 * 1030 4 * 10-5 = 2 * 1025

In Exercises 133140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. (7 * 105 ) + (2 * 10-3 ) = 9 * 102

In Exercises 133140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. (4 * 103 ) + (3 * 102 ) = 4.3 * 103

The mad Dr. Frankenstein has gathered enough bits and pieces (so to speak) for 2-1 + 2-2 of his creature-to-be. Write a fraction that represents the amount of his creature that must still be obtained.

If bA = MN, bC = M, and bD = N, what is the relationship among A, C, and D?

Our hearts beat approximately 70 times per minute. Express in scientific notation how many times the heart beats over a lifetime of 80 years. Round the decimal factor in your scientific notation answer to two decimal places.

Putting Numbers into Perspective. A large number can be put into perspective by comparing it with another number. For example, we put the $18.9 trillion national debt in perspective (Example 12) by comparing this number to the number of U.S. citizens. For this project, each group member should consult an almanac, a newspaper, or the Internet to find a number greater than one million. Explain to other members of the group the context in which the large number is used. Express the number in scientific notation. Then put the number into perspective by comparing it with another number.

Exercises 145147 will help you prepare for the material covered in the next section. a. Find 216 # 24. b. Find 216 # 4. c. Based on your answers to parts (a) and (b), what can you conclude?

Exercises 145147 will help you prepare for the material covered in the next section. a. Use a calculator to approximate 2300 to two decimal places. b. Use a calculator to approximate 1023 to two decimal places. c. Based on your answers to parts (a) and (b), what can you conclude?

Exercises 145147 will help you prepare for the material covered in the next section. a. Simplify: 21x + 10x. b. Simplify: 2122 + 1022.