LESSON 7.2 N Practice A AME ATE

LESSON

7.2

NAME _________________________________________________________ DATE ___________

Practice A

For use with pages 407?414

Simplify the expression using the properties of rational exponents.

1. 413 443

2. 63413

3. 5 323

4. 1354

1056 5. 1046

2 18

6. 3

Simplify the expression using the properties of radicals.

7. 7 3

8. 3 5

1

10.

25

11. 5 3

20 9. 5

12. 6 30

10

Simplify the expression. Assume all variables are positive.

13. x14 x24

14. x234

16. 3x12

17. 27x13

x53 19. x23

x12 20. x52

15. x3516 18. x72

100 12

21. x

Perform the indicated operation. Assume all variables are positive.

22. 23 43

23. 57 37

24. 6 5 22 9 5 22

25. 2x 7x

26. 5 3 x 2 3 x

27. 8 4 x 6 4 x

Write the expression in simplest form. Assume all variables are positive.

28. 49x3

x2

29.

y3

30. 4 x3y5z8

31. 3 x3yz 3 8x3yz

32. x5 5xx3

x2y4z 33. x5

34. Geometry The area of an equilateral triangle is given by A 3 s 2. 4

Find the length of the side s of an equilateral triangle with an area of 12 square inches.

Lesson 7.2

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Algebra 2

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Chapter 7 Resource Book

Answer Key

Chapter 7 Lesson 7.2

Practice A

1. 453

2. 614 3. 523

323

1 4. 1354

5. 1016

218 6. 318

7. 21

8. 6 5

9. 2

10.

1 5

11. 1 0 3

12. 32

13. x34

14. x83 15. x110 16. 3 x12 17. 3x13

1

1

10

18. x72 19. x 20. x2 21. x12 22. 63

23. 27 24. 15 5 22 25. 5x

26. 3 3 x 27. 2 4 x 28. 7x 3 x

29.

x yy

xy y2

30. yz2x3y

31. 3x 3 yz

32. 6x2x

33.

y2xz x2

34. 22 in.

LESSON

7.2

NAME _________________________________________________________ DATE ___________

Practice B

For use with pages 407?414

Simplify the expression using the properties of radicals and rational exponents.

1. 523 543

312 2. 3

4. 314 414

5. 3 2 3 4

3 3 7. 3

64 13

8. 125

3. 72352 4 240

6. 4 15 9. 101223

Simplify the expression. Assume all variables are positive.

10. 9x2

11. 3 2x3

x 12

13. 4

14. 16x14

12x2 16. 3

19. x3 x5

x3 22. x53

1 17. x213

20. x3 3

23. x2

12. x23 x13 15. 5 27x 5 9x4

18. 4 256xy4 21. 4x2 24. 3x6 2x6

Perform the indicated operation.

25. 2 3 3 3 3

26. 3 4 15 2 4 15

27. 3213 5213

28. 42 8

29. 3 40 3 5

30. 5 96 4 5 3

31. Milky Way The Milky Way is 105 light years in diameter and 104 light years in thickness. One light year is equivalent to 5.88 1012 miles. What is the diameter and thickness of the Milky Way in miles?

Archery Target In Exercises 32?34, use the following information.

The figure at the right shows a National Field Archer's Association official hunter's target. The area of the entire hunter's target is approximately 490.9 square inches. The area of the center white circle is approximately 19.6 square inches.

32. Find the radius of the target.

33. Find the radius of the center white circle.

34. Find the ratio of the radius of the white circle to the radius of the target.

Lesson 7.2

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Algebra 2

Chapter 7 Resource Book

Copyright ? McDougal Littell Inc. All rights reserved.

Answer Key

Chapter 7 Lesson 7.2

Practice B

1. 52 25 2. 312 3. 753 4. 1214

5. 3 8 2

6. 2

7. 323

8.

4 5

9. 1013

10. 3x 11. 3 2 x

12. x

x12 13. 2

14. 2x14

15. 3x 16. 2x 17. x23 18. 4y 4 x

19. x35 20. x3 21. 42x2

22.

x43

1 x43

1 23. x2

24. x6

25. 3 3 3 26. 4 15 27. 8213 28. 22

29. 3 3 5 30. 2 5 3

31. diameter 5.88 1017 miles; thickness 5.88 1016 miles 32. 12.5 in.

33. 2.5 in. 34. 0.2

Lesson 7.2

LESSON

7.2

NAME _________________________________________________________ DATE ___________

Practice C

For use with pages 407?414

Simplify the expressions using the properties of radicals and rational exponents.

1. 312 52332

2. 213 23412

612 35

4. 613

312 3

5. 1212

108

7.

27

8. 7 223 224

3. 523152

6. 4 3 2

3 18

3

9.

5

Simplify the expression. Assume all the variables are positive.

x54 y23 10. xy

3x14 y23z 2

11. 2xy12

3xy12 1

13. 27x2y12

14. 5 2x232x27

x43y5 14

12. 16z12

15. 3 4x 3 x

Perform the indicated operations. Assume all variables are positive.

16. 46 36

17. 3 8x6y2z x 3 27x3y2z

18. 5 x 5 32x

19. 3 5 y

9 y2

20. 5 y 1 0 y2 3 1 5 y3

21. xy3x2y3xy 6x3yx54y2

Halley's Comet In Exercises 22 and 23, use the following information.

Halley's Comet travels in an elliptical orbit around the sun, making one complete orbit every 76 years. When the comet was closest to the sun 8.9 1010 meters), it developed its tail. In the diagram at the right, a is the length of the semi-major axis, A is the comet's closest distance to the sun, and B is the comet's furthest distance to the sun.

A Sun

B

22. The length of the semi-major axis a can be found by the

equation a

GMT 2 13 4 2 where

G gravitational constant 6.67 1011 N m2kg2

M mass of sun 1.99 1030 kg

T period 2.4 109 seconds (76 years).

Find the length of the semi-major axis.

23. The comet's farthest distance from the sun can be calculated by B 2a A. What's the comet's farthest distance from the sun?

Halley's Comet a

Not drawn to scale.

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Algebra 2

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Chapter 7 Resource Book

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