skills practice p. application practice p. skills practice...
TRANSCRIPT
Name: Date Period
ExercisesExercises
30 Chapter 1 Foundations for Functions
GUIDED PRACTICESEE EXAMPLE 1 p. 27
Write an algebraic expression to represent each situation.
1. the cost of c containers of yogurt at $0.79 each
2. the area of a rectangle with length ! meters and width 8 meters
SEE EXAMPLE 2 p. 28
Evaluate each expression for the given values of the variables.
3. a 2 + b 2 - 2ab for a = 5 and b = 8 4. 3xy __
x 2 - 9y + 2 for x = 2 and y = 4
SEE EXAMPLE 3 p. 28
Simplify each expression.
5. -8a + 9 - 5a + a 6. -2 (2x + y) - 7x + 2y 7. 1 + (ab - 5a) 5 - b 2
SEE EXAMPLE 4 p. 29
8. Athletics Regan runs and bicycles every day for a total of 60 minutes. Her body uses 9 Calories per minute during running and 7 Calories per minute during bicycling.
a. Write and simplify an expression for the total Calories Regan uses running and bicycling each day.
b. How many Calories does she use on a day when she runs for 20 minutes?
PRACTICE AND PROBLEM SOLVING
For See Exercises Example
9–10 1 11–14 2 15–18 3 19 4
Independent Practice Write an algebraic expression to represent each situation.
9. the measure of the supplement of an angle whose measure is x°
10. the number of $0.60 bagels that can be purchased with d dollars
Evaluate each expression for the given values of the variables.
11. 6c - 3 c 2 + d 3 for c = 5 and d = 3 12. y 2 - 2 xy 2 - x for x = 2 and y = 3
13. 3 a 2 b - a b 3 + 5 for a = 5 and b = 2 14. 2s - t 2 _ s t 2
for s = 5 and t = 3
Simplify each expression.
15. -x - 3y + 4x - 9y + 2 16. -4 (-a + 3b) - 3 (a - 5b)
17. 5 - (3m + 2n) 18. x (4 + y) - 2x (y + 7)
19. Home Economics Enrique is baking muffins and bread. He wants to bake a total of 10 batches. Each batch of muffins bakes for 30 minutes, and each batch of bread bakes for 50 minutes. Let m represent the number of batches of muffins.
a. Write an expression for the total time required to bake a combination of muffins and bread if each batch is baked separately.
b. If Enrique makes 2 batches of muffins, how long will it take to bake all 10 batches?
Simplify each expression. Then evaluate the expression for the given values of the variables.
20. -a ( a 2 + 2a - 1) for a = 2 21. (2g - 1) 2 - 2g + g 2 for g = 3
22. u 2 - v 2 _ uv for u = 4 and v = 2 23. a 2 - 2 ( b 2 - a)
__ 2 + a
for a = 3 and b = 5
KEYWORD: MB7 1-4
1-4
KEYWORD: MB7 Parent
Skills Practice p. S4Application Practice p. S32
Extra Practice
a207se_c01l04_0027_0032.indd 30a207se_c01l04_0027_0032.indd 30 9/8/05 2:43:18 PM9/8/05 2:43:18 PM
Homework 1.5 (9/26/14)
ExercisesExercises
30 Chapter 1 Foundations for Functions
GUIDED PRACTICESEE EXAMPLE 1 p. 27
Write an algebraic expression to represent each situation.
1. the cost of c containers of yogurt at $0.79 each
2. the area of a rectangle with length ! meters and width 8 meters
SEE EXAMPLE 2 p. 28
Evaluate each expression for the given values of the variables.
3. a 2 + b 2 - 2ab for a = 5 and b = 8 4. 3xy __
x 2 - 9y + 2 for x = 2 and y = 4
SEE EXAMPLE 3 p. 28
Simplify each expression.
5. -8a + 9 - 5a + a 6. -2 (2x + y) - 7x + 2y 7. 1 + (ab - 5a) 5 - b 2
SEE EXAMPLE 4 p. 29
8. Athletics Regan runs and bicycles every day for a total of 60 minutes. Her body uses 9 Calories per minute during running and 7 Calories per minute during bicycling.
a. Write and simplify an expression for the total Calories Regan uses running and bicycling each day.
b. How many Calories does she use on a day when she runs for 20 minutes?
PRACTICE AND PROBLEM SOLVING
For See Exercises Example
9–10 1 11–14 2 15–18 3 19 4
Independent Practice Write an algebraic expression to represent each situation.
9. the measure of the supplement of an angle whose measure is x°
10. the number of $0.60 bagels that can be purchased with d dollars
Evaluate each expression for the given values of the variables.
11. 6c - 3 c 2 + d 3 for c = 5 and d = 3 12. y 2 - 2 xy 2 - x for x = 2 and y = 3
13. 3 a 2 b - a b 3 + 5 for a = 5 and b = 2 14. 2s - t 2 _ s t 2
for s = 5 and t = 3
Simplify each expression.
15. -x - 3y + 4x - 9y + 2 16. -4 (-a + 3b) - 3 (a - 5b)
17. 5 - (3m + 2n) 18. x (4 + y) - 2x (y + 7)
19. Home Economics Enrique is baking muffins and bread. He wants to bake a total of 10 batches. Each batch of muffins bakes for 30 minutes, and each batch of bread bakes for 50 minutes. Let m represent the number of batches of muffins.
a. Write an expression for the total time required to bake a combination of muffins and bread if each batch is baked separately.
b. If Enrique makes 2 batches of muffins, how long will it take to bake all 10 batches?
Simplify each expression. Then evaluate the expression for the given values of the variables.
20. -a ( a 2 + 2a - 1) for a = 2 21. (2g - 1) 2 - 2g + g 2 for g = 3
22. u 2 - v 2 _ uv for u = 4 and v = 2 23. a 2 - 2 ( b 2 - a)
__ 2 + a
for a = 3 and b = 5
KEYWORD: MB7 1-4
1-4
KEYWORD: MB7 Parent
Skills Practice p. S4Application Practice p. S32
Extra Practice
a207se_c01l04_0027_0032.indd 30a207se_c01l04_0027_0032.indd 30 9/8/05 2:43:18 PM9/8/05 2:43:18 PM
ExercisesExercises
30 Chapter 1 Foundations for Functions
GUIDED PRACTICESEE EXAMPLE 1 p. 27
Write an algebraic expression to represent each situation.
1. the cost of c containers of yogurt at $0.79 each
2. the area of a rectangle with length ! meters and width 8 meters
SEE EXAMPLE 2 p. 28
Evaluate each expression for the given values of the variables.
3. a 2 + b 2 - 2ab for a = 5 and b = 8 4. 3xy __
x 2 - 9y + 2 for x = 2 and y = 4
SEE EXAMPLE 3 p. 28
Simplify each expression.
5. -8a + 9 - 5a + a 6. -2 (2x + y) - 7x + 2y 7. 1 + (ab - 5a) 5 - b 2
SEE EXAMPLE 4 p. 29
8. Athletics Regan runs and bicycles every day for a total of 60 minutes. Her body uses 9 Calories per minute during running and 7 Calories per minute during bicycling.
a. Write and simplify an expression for the total Calories Regan uses running and bicycling each day.
b. How many Calories does she use on a day when she runs for 20 minutes?
PRACTICE AND PROBLEM SOLVING
For See Exercises Example
9–10 1 11–14 2 15–18 3 19 4
Independent Practice Write an algebraic expression to represent each situation.
9. the measure of the supplement of an angle whose measure is x°
10. the number of $0.60 bagels that can be purchased with d dollars
Evaluate each expression for the given values of the variables.
11. 6c - 3 c 2 + d 3 for c = 5 and d = 3 12. y 2 - 2 xy 2 - x for x = 2 and y = 3
13. 3 a 2 b - a b 3 + 5 for a = 5 and b = 2 14. 2s - t 2 _ s t 2
for s = 5 and t = 3
Simplify each expression.
15. -x - 3y + 4x - 9y + 2 16. -4 (-a + 3b) - 3 (a - 5b)
17. 5 - (3m + 2n) 18. x (4 + y) - 2x (y + 7)
19. Home Economics Enrique is baking muffins and bread. He wants to bake a total of 10 batches. Each batch of muffins bakes for 30 minutes, and each batch of bread bakes for 50 minutes. Let m represent the number of batches of muffins.
a. Write an expression for the total time required to bake a combination of muffins and bread if each batch is baked separately.
b. If Enrique makes 2 batches of muffins, how long will it take to bake all 10 batches?
Simplify each expression. Then evaluate the expression for the given values of the variables.
20. -a ( a 2 + 2a - 1) for a = 2 21. (2g - 1) 2 - 2g + g 2 for g = 3
22. u 2 - v 2 _ uv for u = 4 and v = 2 23. a 2 - 2 ( b 2 - a)
__ 2 + a
for a = 3 and b = 5
KEYWORD: MB7 1-4
1-4
KEYWORD: MB7 Parent
Skills Practice p. S4Application Practice p. S32
Extra Practice
a207se_c01l04_0027_0032.indd 30a207se_c01l04_0027_0032.indd 30 9/8/05 2:43:18 PM9/8/05 2:43:18 PM
ExercisesExercises
30 Chapter 1 Foundations for Functions
GUIDED PRACTICESEE EXAMPLE 1 p. 27
Write an algebraic expression to represent each situation.
1. the cost of c containers of yogurt at $0.79 each
2. the area of a rectangle with length ! meters and width 8 meters
SEE EXAMPLE 2 p. 28
Evaluate each expression for the given values of the variables.
3. a 2 + b 2 - 2ab for a = 5 and b = 8 4. 3xy __
x 2 - 9y + 2 for x = 2 and y = 4
SEE EXAMPLE 3 p. 28
Simplify each expression.
5. -8a + 9 - 5a + a 6. -2 (2x + y) - 7x + 2y 7. 1 + (ab - 5a) 5 - b 2
SEE EXAMPLE 4 p. 29
8. Athletics Regan runs and bicycles every day for a total of 60 minutes. Her body uses 9 Calories per minute during running and 7 Calories per minute during bicycling.
a. Write and simplify an expression for the total Calories Regan uses running and bicycling each day.
b. How many Calories does she use on a day when she runs for 20 minutes?
PRACTICE AND PROBLEM SOLVING
For See Exercises Example
9–10 1 11–14 2 15–18 3 19 4
Independent Practice Write an algebraic expression to represent each situation.
9. the measure of the supplement of an angle whose measure is x°
10. the number of $0.60 bagels that can be purchased with d dollars
Evaluate each expression for the given values of the variables.
11. 6c - 3 c 2 + d 3 for c = 5 and d = 3 12. y 2 - 2 xy 2 - x for x = 2 and y = 3
13. 3 a 2 b - a b 3 + 5 for a = 5 and b = 2 14. 2s - t 2 _ s t 2
for s = 5 and t = 3
Simplify each expression.
15. -x - 3y + 4x - 9y + 2 16. -4 (-a + 3b) - 3 (a - 5b)
17. 5 - (3m + 2n) 18. x (4 + y) - 2x (y + 7)
19. Home Economics Enrique is baking muffins and bread. He wants to bake a total of 10 batches. Each batch of muffins bakes for 30 minutes, and each batch of bread bakes for 50 minutes. Let m represent the number of batches of muffins.
a. Write an expression for the total time required to bake a combination of muffins and bread if each batch is baked separately.
b. If Enrique makes 2 batches of muffins, how long will it take to bake all 10 batches?
Simplify each expression. Then evaluate the expression for the given values of the variables.
20. -a ( a 2 + 2a - 1) for a = 2 21. (2g - 1) 2 - 2g + g 2 for g = 3
22. u 2 - v 2 _ uv for u = 4 and v = 2 23. a 2 - 2 ( b 2 - a)
__ 2 + a
for a = 3 and b = 5
KEYWORD: MB7 1-4
1-4
KEYWORD: MB7 Parent
Skills Practice p. S4Application Practice p. S32
Extra Practice
a207se_c01l04_0027_0032.indd 30a207se_c01l04_0027_0032.indd 30 9/8/05 2:43:18 PM9/8/05 2:43:18 PM
ExercisesExercises
30 Chapter 1 Foundations for Functions
GUIDED PRACTICESEE EXAMPLE 1 p. 27
Write an algebraic expression to represent each situation.
1. the cost of c containers of yogurt at $0.79 each
2. the area of a rectangle with length ! meters and width 8 meters
SEE EXAMPLE 2 p. 28
Evaluate each expression for the given values of the variables.
3. a 2 + b 2 - 2ab for a = 5 and b = 8 4. 3xy __
x 2 - 9y + 2 for x = 2 and y = 4
SEE EXAMPLE 3 p. 28
Simplify each expression.
5. -8a + 9 - 5a + a 6. -2 (2x + y) - 7x + 2y 7. 1 + (ab - 5a) 5 - b 2
SEE EXAMPLE 4 p. 29
8. Athletics Regan runs and bicycles every day for a total of 60 minutes. Her body uses 9 Calories per minute during running and 7 Calories per minute during bicycling.
a. Write and simplify an expression for the total Calories Regan uses running and bicycling each day.
b. How many Calories does she use on a day when she runs for 20 minutes?
PRACTICE AND PROBLEM SOLVING
For See Exercises Example
9–10 1 11–14 2 15–18 3 19 4
Independent Practice Write an algebraic expression to represent each situation.
9. the measure of the supplement of an angle whose measure is x°
10. the number of $0.60 bagels that can be purchased with d dollars
Evaluate each expression for the given values of the variables.
11. 6c - 3 c 2 + d 3 for c = 5 and d = 3 12. y 2 - 2 xy 2 - x for x = 2 and y = 3
13. 3 a 2 b - a b 3 + 5 for a = 5 and b = 2 14. 2s - t 2 _ s t 2
for s = 5 and t = 3
Simplify each expression.
15. -x - 3y + 4x - 9y + 2 16. -4 (-a + 3b) - 3 (a - 5b)
17. 5 - (3m + 2n) 18. x (4 + y) - 2x (y + 7)
19. Home Economics Enrique is baking muffins and bread. He wants to bake a total of 10 batches. Each batch of muffins bakes for 30 minutes, and each batch of bread bakes for 50 minutes. Let m represent the number of batches of muffins.
a. Write an expression for the total time required to bake a combination of muffins and bread if each batch is baked separately.
b. If Enrique makes 2 batches of muffins, how long will it take to bake all 10 batches?
Simplify each expression. Then evaluate the expression for the given values of the variables.
20. -a ( a 2 + 2a - 1) for a = 2 21. (2g - 1) 2 - 2g + g 2 for g = 3
22. u 2 - v 2 _ uv for u = 4 and v = 2 23. a 2 - 2 ( b 2 - a)
__ 2 + a
for a = 3 and b = 5
KEYWORD: MB7 1-4
1-4
KEYWORD: MB7 Parent
Skills Practice p. S4Application Practice p. S32
Extra Practice
a207se_c01l04_0027_0032.indd 30a207se_c01l04_0027_0032.indd 30 9/8/05 2:43:18 PM9/8/05 2:43:18 PM
38 Chapter 1 Foundations for Functions
THINK AND DISCUSS 1. Tell which properties of exponents apply only to expressions with the
same base.
2. List the steps for writing a number in scientific notation.
3. GET ORGANIZED Copy and complete the graphic organizer by providing a numerical and algebraic example of each property.
KEYWORD: MB7 1-5
KEYWORD: MB7 Parent
1-5 ExercisesExercises
GUIDED PRACTICE 1. Vocabulary Describe the requirements for a number to be expressed in scientific
notation.
SEE EXAMPLE 1 p. 34
Write each expression in expanded form.
2. 4 (a - b) 2 3. (12xy) 4 4. - s 3 (-2t) 5 5. (- 1 _ 2
d) 3
SEE EXAMPLE 2 p. 35
Simplify each expression.
6. (- 3 _ 5
) -2
7. 5 0 8. ( 2 _ 3
) -3
9. 10 -1
SEE EXAMPLE 3 p. 36
Simplify each expression. Assume all variables are nonzero.
10. (-3 a 2 b 3 ) 2 11. c 3 d 2 ( c -2 d 4 ) 12. 5 uv 6 _
u 2 v 2 13. 10 (
y 5 _
x 2 )
2
14. -2 s -3 t (7 s -8 t 5 ) 15. -4m (m n 2 ) 3 16.
(4b) 2 _
2b 17.
x -1 y -2 _
x 3 y -5
SEE EXAMPLE 4 p. 36
Simplify each expression. Write the answer in scientific notation.
18. (2.2 ! 10 5 ) (4.5 ! 10 11 ) 19. 7.8 ! 10 8 _ 2.6 ! 10 -3
20. 16 ! 10 -3 _ 4.0 ! 10 4
SEE EXAMPLE 5 p. 37
21. Technology Nanotechnology is a branch of engineering that works with devices that are smaller than 100 nanometers. The width of one string on the playable nanoguitar created by scientists at Cornell University in 2003 is 2.0 ! 10 -7 meters. If the width of a human hair is about 80 microns, how many nanoguitar strings would have the same width as a human hair? (Hint: 1 micron = 10 -6 meters)
a207se_c01l05_0034_0041.indd 38a207se_c01l05_0034_0041.indd 38 9/8/05 2:45:33 PM9/8/05 2:45:33 PM
38 Chapter 1 Foundations for Functions
THINK AND DISCUSS 1. Tell which properties of exponents apply only to expressions with the
same base.
2. List the steps for writing a number in scientific notation.
3. GET ORGANIZED Copy and complete the graphic organizer by providing a numerical and algebraic example of each property.
KEYWORD: MB7 1-5
KEYWORD: MB7 Parent
1-5 ExercisesExercises
GUIDED PRACTICE 1. Vocabulary Describe the requirements for a number to be expressed in scientific
notation.
SEE EXAMPLE 1 p. 34
Write each expression in expanded form.
2. 4 (a - b) 2 3. (12xy) 4 4. - s 3 (-2t) 5 5. (- 1 _ 2
d) 3
SEE EXAMPLE 2 p. 35
Simplify each expression.
6. (- 3 _ 5
) -2
7. 5 0 8. ( 2 _ 3
) -3
9. 10 -1
SEE EXAMPLE 3 p. 36
Simplify each expression. Assume all variables are nonzero.
10. (-3 a 2 b 3 ) 2 11. c 3 d 2 ( c -2 d 4 ) 12. 5 uv 6 _
u 2 v 2 13. 10 (
y 5 _
x 2 )
2
14. -2 s -3 t (7 s -8 t 5 ) 15. -4m (m n 2 ) 3 16.
(4b) 2 _
2b 17.
x -1 y -2 _
x 3 y -5
SEE EXAMPLE 4 p. 36
Simplify each expression. Write the answer in scientific notation.
18. (2.2 ! 10 5 ) (4.5 ! 10 11 ) 19. 7.8 ! 10 8 _ 2.6 ! 10 -3
20. 16 ! 10 -3 _ 4.0 ! 10 4
SEE EXAMPLE 5 p. 37
21. Technology Nanotechnology is a branch of engineering that works with devices that are smaller than 100 nanometers. The width of one string on the playable nanoguitar created by scientists at Cornell University in 2003 is 2.0 ! 10 -7 meters. If the width of a human hair is about 80 microns, how many nanoguitar strings would have the same width as a human hair? (Hint: 1 micron = 10 -6 meters)
a207se_c01l05_0034_0041.indd 38a207se_c01l05_0034_0041.indd 38 9/8/05 2:45:33 PM9/8/05 2:45:33 PM
38 Chapter 1 Foundations for Functions
THINK AND DISCUSS 1. Tell which properties of exponents apply only to expressions with the
same base.
2. List the steps for writing a number in scientific notation.
3. GET ORGANIZED Copy and complete the graphic organizer by providing a numerical and algebraic example of each property.
KEYWORD: MB7 1-5
KEYWORD: MB7 Parent
1-5 ExercisesExercises
GUIDED PRACTICE 1. Vocabulary Describe the requirements for a number to be expressed in scientific
notation.
SEE EXAMPLE 1 p. 34
Write each expression in expanded form.
2. 4 (a - b) 2 3. (12xy) 4 4. - s 3 (-2t) 5 5. (- 1 _ 2
d) 3
SEE EXAMPLE 2 p. 35
Simplify each expression.
6. (- 3 _ 5
) -2
7. 5 0 8. ( 2 _ 3
) -3
9. 10 -1
SEE EXAMPLE 3 p. 36
Simplify each expression. Assume all variables are nonzero.
10. (-3 a 2 b 3 ) 2 11. c 3 d 2 ( c -2 d 4 ) 12. 5 uv 6 _
u 2 v 2 13. 10 (
y 5 _
x 2 )
2
14. -2 s -3 t (7 s -8 t 5 ) 15. -4m (m n 2 ) 3 16.
(4b) 2 _
2b 17.
x -1 y -2 _
x 3 y -5
SEE EXAMPLE 4 p. 36
Simplify each expression. Write the answer in scientific notation.
18. (2.2 ! 10 5 ) (4.5 ! 10 11 ) 19. 7.8 ! 10 8 _ 2.6 ! 10 -3
20. 16 ! 10 -3 _ 4.0 ! 10 4
SEE EXAMPLE 5 p. 37
21. Technology Nanotechnology is a branch of engineering that works with devices that are smaller than 100 nanometers. The width of one string on the playable nanoguitar created by scientists at Cornell University in 2003 is 2.0 ! 10 -7 meters. If the width of a human hair is about 80 microns, how many nanoguitar strings would have the same width as a human hair? (Hint: 1 micron = 10 -6 meters)
a207se_c01l05_0034_0041.indd 38a207se_c01l05_0034_0041.indd 38 9/8/05 2:45:33 PM9/8/05 2:45:33 PM
38 Chapter 1 Foundations for Functions
THINK AND DISCUSS 1. Tell which properties of exponents apply only to expressions with the
same base.
2. List the steps for writing a number in scientific notation.
3. GET ORGANIZED Copy and complete the graphic organizer by providing a numerical and algebraic example of each property.
KEYWORD: MB7 1-5
KEYWORD: MB7 Parent
1-5 ExercisesExercises
GUIDED PRACTICE 1. Vocabulary Describe the requirements for a number to be expressed in scientific
notation.
SEE EXAMPLE 1 p. 34
Write each expression in expanded form.
2. 4 (a - b) 2 3. (12xy) 4 4. - s 3 (-2t) 5 5. (- 1 _ 2
d) 3
SEE EXAMPLE 2 p. 35
Simplify each expression.
6. (- 3 _ 5
) -2
7. 5 0 8. ( 2 _ 3
) -3
9. 10 -1
SEE EXAMPLE 3 p. 36
Simplify each expression. Assume all variables are nonzero.
10. (-3 a 2 b 3 ) 2 11. c 3 d 2 ( c -2 d 4 ) 12. 5 uv 6 _
u 2 v 2 13. 10 (
y 5 _
x 2 )
2
14. -2 s -3 t (7 s -8 t 5 ) 15. -4m (m n 2 ) 3 16.
(4b) 2 _
2b 17.
x -1 y -2 _
x 3 y -5
SEE EXAMPLE 4 p. 36
Simplify each expression. Write the answer in scientific notation.
18. (2.2 ! 10 5 ) (4.5 ! 10 11 ) 19. 7.8 ! 10 8 _ 2.6 ! 10 -3
20. 16 ! 10 -3 _ 4.0 ! 10 4
SEE EXAMPLE 5 p. 37
21. Technology Nanotechnology is a branch of engineering that works with devices that are smaller than 100 nanometers. The width of one string on the playable nanoguitar created by scientists at Cornell University in 2003 is 2.0 ! 10 -7 meters. If the width of a human hair is about 80 microns, how many nanoguitar strings would have the same width as a human hair? (Hint: 1 micron = 10 -6 meters)
a207se_c01l05_0034_0041.indd 38a207se_c01l05_0034_0041.indd 38 9/8/05 2:45:33 PM9/8/05 2:45:33 PM
38 Chapter 1 Foundations for Functions
THINK AND DISCUSS 1. Tell which properties of exponents apply only to expressions with the
same base.
2. List the steps for writing a number in scientific notation.
3. GET ORGANIZED Copy and complete the graphic organizer by providing a numerical and algebraic example of each property.
KEYWORD: MB7 1-5
KEYWORD: MB7 Parent
1-5 ExercisesExercises
GUIDED PRACTICE 1. Vocabulary Describe the requirements for a number to be expressed in scientific
notation.
SEE EXAMPLE 1 p. 34
Write each expression in expanded form.
2. 4 (a - b) 2 3. (12xy) 4 4. - s 3 (-2t) 5 5. (- 1 _ 2
d) 3
SEE EXAMPLE 2 p. 35
Simplify each expression.
6. (- 3 _ 5
) -2
7. 5 0 8. ( 2 _ 3
) -3
9. 10 -1
SEE EXAMPLE 3 p. 36
Simplify each expression. Assume all variables are nonzero.
10. (-3 a 2 b 3 ) 2 11. c 3 d 2 ( c -2 d 4 ) 12. 5 uv 6 _
u 2 v 2 13. 10 (
y 5 _
x 2 )
2
14. -2 s -3 t (7 s -8 t 5 ) 15. -4m (m n 2 ) 3 16.
(4b) 2 _
2b 17.
x -1 y -2 _
x 3 y -5
SEE EXAMPLE 4 p. 36
Simplify each expression. Write the answer in scientific notation.
18. (2.2 ! 10 5 ) (4.5 ! 10 11 ) 19. 7.8 ! 10 8 _ 2.6 ! 10 -3
20. 16 ! 10 -3 _ 4.0 ! 10 4
SEE EXAMPLE 5 p. 37
21. Technology Nanotechnology is a branch of engineering that works with devices that are smaller than 100 nanometers. The width of one string on the playable nanoguitar created by scientists at Cornell University in 2003 is 2.0 ! 10 -7 meters. If the width of a human hair is about 80 microns, how many nanoguitar strings would have the same width as a human hair? (Hint: 1 micron = 10 -6 meters)
a207se_c01l05_0034_0041.indd 38a207se_c01l05_0034_0041.indd 38 9/8/05 2:45:33 PM9/8/05 2:45:33 PM38 Chapter 1 Foundations for Functions
THINK AND DISCUSS 1. Tell which properties of exponents apply only to expressions with the
same base.
2. List the steps for writing a number in scientific notation.
3. GET ORGANIZED Copy and complete the graphic organizer by providing a numerical and algebraic example of each property.
KEYWORD: MB7 1-5
KEYWORD: MB7 Parent
1-5 ExercisesExercises
GUIDED PRACTICE 1. Vocabulary Describe the requirements for a number to be expressed in scientific
notation.
SEE EXAMPLE 1 p. 34
Write each expression in expanded form.
2. 4 (a - b) 2 3. (12xy) 4 4. - s 3 (-2t) 5 5. (- 1 _ 2
d) 3
SEE EXAMPLE 2 p. 35
Simplify each expression.
6. (- 3 _ 5
) -2
7. 5 0 8. ( 2 _ 3
) -3
9. 10 -1
SEE EXAMPLE 3 p. 36
Simplify each expression. Assume all variables are nonzero.
10. (-3 a 2 b 3 ) 2 11. c 3 d 2 ( c -2 d 4 ) 12. 5 uv 6 _
u 2 v 2 13. 10 (
y 5 _
x 2 )
2
14. -2 s -3 t (7 s -8 t 5 ) 15. -4m (m n 2 ) 3 16.
(4b) 2 _
2b 17.
x -1 y -2 _
x 3 y -5
SEE EXAMPLE 4 p. 36
Simplify each expression. Write the answer in scientific notation.
18. (2.2 ! 10 5 ) (4.5 ! 10 11 ) 19. 7.8 ! 10 8 _ 2.6 ! 10 -3
20. 16 ! 10 -3 _ 4.0 ! 10 4
SEE EXAMPLE 5 p. 37
21. Technology Nanotechnology is a branch of engineering that works with devices that are smaller than 100 nanometers. The width of one string on the playable nanoguitar created by scientists at Cornell University in 2003 is 2.0 ! 10 -7 meters. If the width of a human hair is about 80 microns, how many nanoguitar strings would have the same width as a human hair? (Hint: 1 micron = 10 -6 meters)
a207se_c01l05_0034_0041.indd 38a207se_c01l05_0034_0041.indd 38 9/8/05 2:45:33 PM9/8/05 2:45:33 PM
38 Chapter 1 Foundations for Functions
THINK AND DISCUSS 1. Tell which properties of exponents apply only to expressions with the
same base.
2. List the steps for writing a number in scientific notation.
3. GET ORGANIZED Copy and complete the graphic organizer by providing a numerical and algebraic example of each property.
KEYWORD: MB7 1-5
KEYWORD: MB7 Parent
1-5 ExercisesExercises
GUIDED PRACTICE 1. Vocabulary Describe the requirements for a number to be expressed in scientific
notation.
SEE EXAMPLE 1 p. 34
Write each expression in expanded form.
2. 4 (a - b) 2 3. (12xy) 4 4. - s 3 (-2t) 5 5. (- 1 _ 2
d) 3
SEE EXAMPLE 2 p. 35
Simplify each expression.
6. (- 3 _ 5
) -2
7. 5 0 8. ( 2 _ 3
) -3
9. 10 -1
SEE EXAMPLE 3 p. 36
Simplify each expression. Assume all variables are nonzero.
10. (-3 a 2 b 3 ) 2 11. c 3 d 2 ( c -2 d 4 ) 12. 5 uv 6 _
u 2 v 2 13. 10 (
y 5 _
x 2 )
2
14. -2 s -3 t (7 s -8 t 5 ) 15. -4m (m n 2 ) 3 16.
(4b) 2 _
2b 17.
x -1 y -2 _
x 3 y -5
SEE EXAMPLE 4 p. 36
Simplify each expression. Write the answer in scientific notation.
18. (2.2 ! 10 5 ) (4.5 ! 10 11 ) 19. 7.8 ! 10 8 _ 2.6 ! 10 -3
20. 16 ! 10 -3 _ 4.0 ! 10 4
SEE EXAMPLE 5 p. 37
21. Technology Nanotechnology is a branch of engineering that works with devices that are smaller than 100 nanometers. The width of one string on the playable nanoguitar created by scientists at Cornell University in 2003 is 2.0 ! 10 -7 meters. If the width of a human hair is about 80 microns, how many nanoguitar strings would have the same width as a human hair? (Hint: 1 micron = 10 -6 meters)
a207se_c01l05_0034_0041.indd 38a207se_c01l05_0034_0041.indd 38 9/8/05 2:45:33 PM9/8/05 2:45:33 PM
38 Chapter 1 Foundations for Functions
THINK AND DISCUSS 1. Tell which properties of exponents apply only to expressions with the
same base.
2. List the steps for writing a number in scientific notation.
3. GET ORGANIZED Copy and complete the graphic organizer by providing a numerical and algebraic example of each property.
KEYWORD: MB7 1-5
KEYWORD: MB7 Parent
1-5 ExercisesExercises
GUIDED PRACTICE 1. Vocabulary Describe the requirements for a number to be expressed in scientific
notation.
SEE EXAMPLE 1 p. 34
Write each expression in expanded form.
2. 4 (a - b) 2 3. (12xy) 4 4. - s 3 (-2t) 5 5. (- 1 _ 2
d) 3
SEE EXAMPLE 2 p. 35
Simplify each expression.
6. (- 3 _ 5
) -2
7. 5 0 8. ( 2 _ 3
) -3
9. 10 -1
SEE EXAMPLE 3 p. 36
Simplify each expression. Assume all variables are nonzero.
10. (-3 a 2 b 3 ) 2 11. c 3 d 2 ( c -2 d 4 ) 12. 5 uv 6 _
u 2 v 2 13. 10 (
y 5 _
x 2 )
2
14. -2 s -3 t (7 s -8 t 5 ) 15. -4m (m n 2 ) 3 16.
(4b) 2 _
2b 17.
x -1 y -2 _
x 3 y -5
SEE EXAMPLE 4 p. 36
Simplify each expression. Write the answer in scientific notation.
18. (2.2 ! 10 5 ) (4.5 ! 10 11 ) 19. 7.8 ! 10 8 _ 2.6 ! 10 -3
20. 16 ! 10 -3 _ 4.0 ! 10 4
SEE EXAMPLE 5 p. 37
21. Technology Nanotechnology is a branch of engineering that works with devices that are smaller than 100 nanometers. The width of one string on the playable nanoguitar created by scientists at Cornell University in 2003 is 2.0 ! 10 -7 meters. If the width of a human hair is about 80 microns, how many nanoguitar strings would have the same width as a human hair? (Hint: 1 micron = 10 -6 meters)
a207se_c01l05_0034_0041.indd 38a207se_c01l05_0034_0041.indd 38 9/8/05 2:45:33 PM9/8/05 2:45:33 PM