In Exercises 6971, simplify using properties of exponents.(125x6)23

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. (3x + 5)(4x - 7)

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. (3x + 5) - (4x - 7)

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 26 + 926

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 3212 - 227

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 7x + 3[9 - (2x - 6)]

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. (8x - 3) 2

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 1x 1 3y - 1 2 26

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. a 2 7 b 0 - 32 - 2 5

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. (2x - 5) - (x2 - 3x + 1)

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. (2x - 5)(x2 - 3x + 1)

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. x3 + x3 - x3 # x3

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. (9a - 10b)(2a + b)

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. {a, c, d, e} {c, d, f, h}

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. {a, c, d, e} {c, d, f, h}

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. (3x2y3 - xy + 4y2 ) - (-2x2y3 - 3xy + 5y2 )

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 24x2y13 -2x5y-2

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. a 1 3 x-5y4 b(18x-2y-1 )

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 212 x4

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 24 * 103 2 * 106 (Express the answer in scientific notation.)

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 13 32 13 2

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. (x3 + 2)(x3 - 2)

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. (x2 + 2) 2

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 250 # 26

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 11 7 - 23

In Exercises 125, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 11 23

List all the rational numbers in this set: e -11, - 3 7 , 0, 0.45, 223,225 f.

In Exercises 2728, rewrite each expression without absolute value bars. 2 - 213 0

In Exercises 2728, rewrite each expression without absolute value bars. x2  x if x 6 0

If the population of the United States is approximately 3.0 * 108 and each person produces about 4.6 pounds of garbage per day, express the total number of pounds of garbage produced in the United States in one day in scientific notation.

A human brain contains 3 * 1010 neurons and a gorilla brain contains 7.5 * 109 neurons. How many times as many neurons are in the brain of a human as in the brain of a gorilla?

College students are graduating with the highest debt burden in history. The bar graph shows the mean, or average, studentloan debt in the United States for five selected graduating years from 2001 through 2013. College students are graduating with the highest debt burden in history. The bar graph shows the mean, or average, studentloan debt in the United States for five selected graduating years from 2001 through 2013.

In Exercises 3233, write each number in decimal notation. 3.74 * 104

In Exercises 3233, write each number in decimal notation. 7.45 * 10-5

In Exercises 3435, write each number in scientific notation. 3,590,000

In Exercises 3435, write each number in scientific notation. 3,590,000

In Exercises 3637, perform the indicated operation and write the answer in decimal notation. (3 * 103 )(1.3 * 102 )

In Exercises 3637, perform the indicated operation and write the answer in decimal notation. 6.9 * 103 3 * 105

In 2009, the United States government spent more than it had collected in taxes, resulting in a budget deficit of $1.35 trillion. In Exercises 3840, you will use scientific notation to put a number like 1.35 trillion in perspective. Use 1012 for 1 trillion. Express 1.35 trillion in scientific notation.

In 2009, the United States government spent more than it had collected in taxes, resulting in a budget deficit of $1.35 trillion. In Exercises 3840, you will use scientific notation to put a number like 1.35 trillion in perspective. Use 1012 for 1 trillion. There are approximately 32,000,000 seconds in a year. Express this number in scientific notation.

In 2009, the United States government spent more than it had collected in taxes, resulting in a budget deficit of $1.35 trillion. In Exercises 3840, you will use scientific notation to put a number like 1.35 trillion in perspective. Use 1012 for 1 trillion. Use your scientific notation answers from Exercises 38 and 39 to answer this question: How many years is 1.35 trillion seconds? Round to the nearest year.

Use the product rule to simplify the expressions in Exercises 4144. In Exercises 4344, assume that variables represent nonnegative real numbers. 2300

Use the product rule to simplify the expressions in Exercises 4144. In Exercises 4344, assume that variables represent nonnegative real numbers. 212x2

Use the product rule to simplify the expressions in Exercises 4144. In Exercises 4344, assume that variables represent nonnegative real numbers. 210x # 22x

Use the product rule to simplify the expressions in Exercises 4144. In Exercises 4344, assume that variables represent nonnegative real numbers. 2r3

Use the quotient rule to simplify the expressions in Exercises 4546. A 121 4

Use the quotient rule to simplify the expressions in Exercises 4546. 296x3 22x (Assume that x 7 0.)

In Exercises 4749, add or subtract terms whenever possible. 725 + 1325

In Exercises 4749, add or subtract terms whenever possible. 2250 + 328

In Exercises 4749, add or subtract terms whenever possible. 4272 - 2248

In Exercises 5053, rationalize the denominator. 30 25

In Exercises 5053, rationalize the denominator. 22 23

In Exercises 5053, rationalize the denominator. 5 6 + 23

In Exercises 5053, rationalize the denominator. 14 27 - 25

Evaluate each expression in Exercises 5457 or indicate that the root is not a real number. 23 125

Evaluate each expression in Exercises 5457 or indicate that the root is not a real number. 25 -32

Evaluate each expression in Exercises 5457 or indicate that the root is not a real number. 24 -125

Evaluate each expression in Exercises 5457 or indicate that the root is not a real number. 24 (-5) 4

Simplify the radical expressions in Exercises 5862. 23 81

Simplify the radical expressions in Exercises 5862. 23 y5

Simplify the radical expressions in Exercises 5862. 24 8 # 24 10

Simplify the radical expressions in Exercises 5862. 423 16 + 523 2

Simplify the radical expressions in Exercises 5862. 24 32x5 24 16x (Assume that x 7 0.)

In Exercises 6368, evaluate each expression. 16 1 2

In Exercises 6368, evaluate each expression. 25 - 1 2

In Exercises 6368, evaluate each expression. 125 1 3

In Exercises 6368, evaluate each expression. 27 - 1 3

In Exercises 6368, evaluate each expression. 64 2 3

In Exercises 6368, evaluate each expression. 27 - 4 3

In Exercises 6971, simplify using properties of exponents. 15x 2 3 2 14x 1 4

In Exercises 6971, simplify using properties of exponents. 15x 3 4 5x 1 2

In Exercises 6971, simplify using properties of exponents. (125x6 ) 2 3

Simplify by reducing the index of the radical: 26 y3 .

In Exercises 7374, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (-6x3 + 7x2 - 9x + 3) + (14x3 + 3x2 - 11x - 7)

In Exercises 7374, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (13x4 - 8x3 + 2x2 ) - (5x4 - 3x3 + 2x2 - 6)

In Exercises 7581, find each product. (3x - 2)(4x2 + 3x - 5)

In Exercises 7581, find each product. (3x - 5)(2x + 1)

In Exercises 7581, find each product. (4x + 5)(4x - 5)

In Exercises 7581, find each product. . (2x + 5) 2

In Exercises 7581, find each product. (3x - 4) 2

In Exercises 7581, find each product. (2x + 1) 3

In Exercises 7581, find each product. (5x - 2) 3

In Exercises 8283, perform the indicated operations. Indicate the degree of the resulting polynomial. (7x2 - 8xy + y2 ) + (-8x2 - 9xy - 4y2 )

In Exercises 8283, perform the indicated operations. Indicate the degree of the resulting polynomial. (13x3y2 - 5x2y - 9x2 ) - (-11x3y2 - 6x2y + 3x2 - 4)

In Exercises 8488, find each product. (x + 7y)(3x - 5y)

In Exercises 8488, find each product. (3x - 5y) 2

In Exercises 8488, find each product. (3x2 + 2y) 2

In Exercises 8488, find each product. (7x + 4y)(7x - 4y)

In Exercises 8488, find each product. (a - b)(a2 + ab + b2 )

In Exercises 89105, factor completely, or state that the polynomial is prime. 15x3 + 3x2

In Exercises 89105, factor completely, or state that the polynomial is prime. x2 - 11x + 28

In Exercises 89105, factor completely, or state that the polynomial is prime. 15x2 - x - 2

In Exercises 89105, factor completely, or state that the polynomial is prime. 64 - x2

In Exercises 89105, factor completely, or state that the polynomial is prime. x2 + 16

In Exercises 89105, factor completely, or state that the polynomial is prime. 3x4 - 9x3 - 30x2

In Exercises 89105, factor completely, or state that the polynomial is prime. 20x7 - 36x3

In Exercises 89105, factor completely, or state that the polynomial is prime. x3 - 3x2 - 9x + 27

In Exercises 89105, factor completely, or state that the polynomial is prime. 16x2 - 40x + 25

In Exercises 89105, factor completely, or state that the polynomial is prime. x4 - 16

In Exercises 89105, factor completely, or state that the polynomial is prime. y3 - 8

In Exercises 89105, factor completely, or state that the polynomial is prime. x3 + 64

In Exercises 89105, factor completely, or state that the polynomial is prime. 3x4 - 12x2

In Exercises 89105, factor completely, or state that the polynomial is prime. 27x3 - 125

In Exercises 89105, factor completely, or state that the polynomial is prime. x5 - x

In Exercises 89105, factor completely, or state that the polynomial is prime. x3 + 5x2 - 2x - 10

In Exercises 89105, factor completely, or state that the polynomial is prime. x2 + 18x + 81 - y2

In Exercises 106108, factor and simplify each algebraic expression. 16x - 3 4 + 32x 1 4

In Exercises 106108, factor and simplify each algebraic expression. (x2 - 4)(x2 + 3) 1 2 - (x2 - 4) 2 (x2 + 3) 3 2

In Exercises 106108, factor and simplify each algebraic expression. 12x - 1 2 + 6x - 3 2

In Exercises 109111, simplify each rational expression. Also, list all numbers that must be excluded from the domain. x3 + 2x2 x + 2

In Exercises 109111, simplify each rational expression. Also, list all numbers that must be excluded from the domain. x2 + 3x - 18 x2 - 36

In Exercises 109111, simplify each rational expression. Also, list all numbers that must be excluded from the domain. x2 + 2x x2 + 4x + 4

In Exercises 112114, multiply or divide as indicated. x2 + 6x + 9 x2 - 4 # x + 3 x - 2

In Exercises 112114, multiply or divide as indicated. 6x + 2 x2 - 1 , 3x2 + x x - 1

In Exercises 112114, multiply or divide as indicated. x2 - 5x - 24 x2 - x - 12 , x2 - 10x + 16 x2 + x - 6

In Exercises 115118, add or subtract as indicated. 2x - 7 x2 - 9 - x - 10 x2 - 9

In Exercises 115118, add or subtract as indicated. 3x x + 2 + x x - 2

In Exercises 115118, add or subtract as indicated. x x2 - 9 + x - 1 x2 - 5x + 6

In Exercises 115118, add or subtract as indicated. 4x - 1 2x2 + 5x - 3 - x + 3 6x2 + x - 2

In Exercises 119121, simplify each complex rational expression. 1 x - 1 2 1 3 - x 6

In Exercises 119121, simplify each complex rational expression. 3 + 12 x 1 - 16 x2

In Exercises 119121, simplify each complex rational expression. 3 - 1 x + 3 3 + 1 x + 3