Download Chapter 3 - Exponents

Chapter 3
Exercise Set 3.1
Simplify the expression, writing it without any negative exponents.
1. (-2x 4 )3
2. (6y)3
3. (-3a 4 bc5 )2
4. -3(-2x 2 )3
5. (-7a 4 )2
6. a2 (a 4 b3c)5
7.
(xy 2 z 3 )4
(x 3 y 2 z)3
(
8.
10. (-x y) z
9.
æ -u 2 v 3 ö
11. ç 4 ÷
è 4u v ø
)
2 4 3
3
(2y 3 )4
2y 5
(2a 3 )2 (3a 4 )
(a 3 )4
æ 2xy 6 z ö
12. ç 2 3 ÷
è xy z ø
2
3
13. (2x 3 )-3
14. (ab2 )-7
15. u3u-9
16. (-2x 5 )-2
17. (x 2 y-3 )-4
18. (-u-4 )3 (2u5 )-2
19. (-4x 2 y-7 )3
20. -3x -2 y (2x 3 y-4 )-2
21. (-2a3b-4c-7 )3
a -3b 4
22. -5 5
a b
æ a -1 ö
23. ç 4 ÷
è 5b ø
2
æ -2a 4 ö
24. ç 2 ÷
è b ø
-2
æ x8 ö
27. ç -2 ÷
èx ø
(
-1
)
2
-3
æ 9y ö
25. ç -5 ÷
èy ø
æ x6 ö
26. ç 2 ÷
è 4x ø
(-a 2 b3 )-2
28.
a -4 b 2
æ x -1 yz -2 ö
29. ç -8 -5 ÷
èx y zø
-1
-2
æ 2a 2 b ö
31. (3ab c) ç 3 ÷
è c ø
2
3
æ x -3 ö
ç ÷
è 2x ø
2
-3
æ xy -2 z -3 ö
30. ç 2 3 -4 ÷
èx y z ø
æ x -4 ö
1
32. x 2 y -5 ç 3 -2 ÷
4
è y ø
2
æ x5 ö
33. ç -3 ÷
è 2y ø
3
æ 6x -8 ö
ç
÷
è y ø
2
Find the value of the algebraic expression at the specified values of its variable or
variables without using a calculator. Simplify the expression before evaluating. Check
your answer using a calculator.
34. x 3 x -4 ; x = 5
35. (x -2 )3; x = -2
36. (2x -1 )3; x = 3
37. (x 2 + y2 )-1; x = -1, y = 2
38. x -2 + y-2 ; x =1, y = 2
39. (x + y)-1; x = 3, y = 5
-2
-1
-1
40. x + y ; x = 3, y = 5
æxö
41. ç ÷ ; x = -2, y = 3
è yø
-2
æxö
42. ç ÷ ; x =1, y = 3
è yø
43.
x -3
44. -2 ; x = 7
x
æ x -2 ö
45. ç
÷ ; x = 3, y = 7
è y ø
x2
; x = -2
x -3
-1
Exercise Set 3.2
Simplify the expression. Assume that all variables represent positive numbers.
1. 12x 6
2.
32x 2 y10
3.
81x 9
4.
25x 5 y 9
7.
8x 5 y17
8.
3x 8 y 5 z 7
5.
24z 7
6. 18y3 z12
9.
20
x 20
10.
x6
y10 z 2
11.
32x 3
9y 2
12.
y 9 z13
w12
14.
49
8x 5
15.
27y8
8z 3
16.
52y8
45z12
18.
x 5 yz 8
x 2 y -5
19.
9x -2 y 6
45x -7 y 2
20.
33x 2 y 6
9x -3
13.
72x 5 y 9
17.
18x 5
2x -2
Find the value of the algebraic expression at the specified values of its variable or
variables in simplified form without a calculator. Simplify the expression before
evaluating. Check your answer using a calculator.
21.
x 3 y 4 ; x = 3, y = 2
22.
x 3 y5 ; x = 4, y = 7
23.
44x 5 ; x = 7
24.
98x 6 ; x = 2
25.
18x 5
; x=4
2x -2
26.
x 3 y -4
; x = 3, y = 5
x 7 y-2
Exercise Set 3.3
Simplify the expression. Assume that all variables represent positive numbers.
3
8x11
2.
3
16x 7
3.
3
40x 6 y 5
4.
3
72x10 y 5
3
48
y12
6.
3
64x 25
y8
7.
3
54x18
y 27
8.
3
32x 28
27y15
1.
5.
Write each radical expression as an exponential expression and each exponential
expression as a radical expression.
9.
1
3
10.
3
72
14. 7-5 2
13. x 2 3
53
11.
15. x 3 5
12.
1
x7
3
16. x -5 3
Evaluate each expression without a calculator. Check your answer using a calculator.
17.
3
8
27
21.
3
-
18.
54
2
25. 81 3
3
-64
19.
5
32
20.
3
-27
3
8
23.
-3
5
96
24.
22.
26. 641 4
5
27. (-32)1 5
1
16
4
3
3
5
40
28. 811 2
Find the value of the algebraic expression at the specified values of its variable or
variables without using a calculator. Check your answer using a calculator.
29. x 2 3; x = 8
30. x 3 4 ; x =16
31. (x 3 y)1 2 ; x = 2, y = 4
32. x 4 3; x = 8
æ x4 ö
33. ç 2 ÷ ; x = 2, y = 3
èy ø
34. (x 2 - y)3 2 ; x = 5, y = -7
35. (x 3 + y3 )5 2 ; x =1, y = 2
36. (xy 2 )-2 3; x = 2, y = -2
32
-5 2
2 -1 2
37. (x + y )
2
; x = 3, y = 4
æ x2 ö
38. ç 2 ÷
èy ø
; x = 3, y = 2