Beginning Algebra, 11th Edition

Summary Exercises on the Rules for Exponents^311

Simplify each expression. Use only positive exponents in your answers. Assume that all

variables represent nonzero real numbers.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   

4. 5. 6.

7. 8. 9.

12 xy-^123

23 x-^3 y^2

13 y-^1 z^32 -^113 y^22

1 y^3 z^22 -^3

5 -^1 + 6 -^1

a

k^4 t^2

k^2 t-^4

b

c^111 c^224 -^2

1 c^3231 c^22 -^6

14 x-^2 y-^32 -^2

a

9 wx^3

y^4

b

3

110 x^2 y^422110 xy^2231 - 2 ab^3 c 241 - 2 a^2 b 23

SUMMARY EXERCISESon the Rules for Exponents

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

22. 23. 24.

25. 26. 27.

28. 29. 30.

31. 32. 33.

34. 35. 36.

37. 38. 39.

40.Concept Check Match each expression (a)–( j) in Column I with the equivalent

expression A–J in Column II. Choices in Column II may be used once, more than once,

or not at all.

III

(a) (b) A. 0 B. 1

(c) (d) C. D. 2

(e) (f ) E. F. 4

(g) (h) G. H.

(i) ( j) I. J.

1

4

-

1

4

2 -^2 , 2 -^120 , 2 -^2

2 -^2 - 2 -^120 # 20 - 2 - 4

1

2

20 # 2 -^221 # 21

20 - 2 -^121 - 20 - 1

20 + 20 21 # 20

a - 1 - 8020

mn-^2 p

m^2 np^4

b

• 2
  a

mn-^2 p

m^2 np^4

b

18 pq-^2243

18 p-^2 q-^323

c 113 x-^6 y 2113 x-^6 y 2 -^1

4 r-^6 s-^2 t

2 r^8 s-^4 t^2

d

• 1
  8 -^1 + 6 -^1

a 15 p-^2 q 2 -^315 pq^324

3 -^4 x-^3

3 -^3 x-^6

b

17 -^1 x-^32 -^21 x^42 -^6 -^2

7 -^1 x-^3

520 - 1 - 820

1 xy 2 -^31 xy 25

1 xy 2 -^4

12 p-^2 qr-^3212 p 2 -^4

a 16 x-^5 z^32 -^3

a^2 b^3 c^4

a-^2 b-^3 c-^4

b

12 xy-^32 -^2 -^2

13 x-^2 y^42 -^3

013

130

- 1 - 1902 - 1 - 1320

a

7 a^2 b^3

2

b

3

c

1 x^43 y^2322

x-^26 y-^42

d

0

5 -^2 + 6 -^2

12 a-^30 b-^29213 a^31 b^302

1 a-^2 b^32 -^4

1 a-^3 b^22 -^21 ab 2 -^4

1 x-^4 y^2231 x^2 y 2 -^1

1 xy^22 -^3

a

• 9 x-^2
  9 x^2

b

• 2
  a

5 x^2

3 x-^4

b

13 -^1 x-^3 y 2 -^112 x^2 y-^322 -^1

15 x-^2 y^22 -^2

a

r^2 st^5

3 r

b

• 2


• 40 + 1 - 420 1 z^42 -^31 z-^22 -^5