1-5 Integer Exponents
Name
Date
Simplify: 52 50
52 50
Identify the bases with negative and zero exponents.
1
1
52
Use the rules for negative and zero exponents.
1
1
25 1 1 25
Remember: Any nonzero exponent raised
to the zero power equals 1. If a ⬆ 0, a0 1.
Remember: For any nonzero number a
1
and any integer n, an n.
a
Simplify.
3
5
Simplify: 2 •6 2
2
35
2
Add exponents to multiply powers with the same base.
26
28
26
286
Remember: For any real number a,
a ⬆ 0, and integers m and n:
am • an amn
am an amn
Simplify.
Subtract exponents to divide powers with the same base.
22
Write in exponential form.
4
Write in standard form and simplify.
Write each expression as repeated multiplication and in exponential form.
Then simplify in standard form.
1. 34
2. 50
3•3•3•3
81
Copyright © by William H. Sadlier, Inc. All rights reserved.
5. 10 • (10) • (10)
53
125
5
1
5
6. 44
7. (5)2 • (5)4
(4 • 4 • 4 • 4)
–256
(10)3
1000
4. 104
3. 5 • 5 • 5
10 • 10 • 10 • 10
10,000
8. 66 62
(5 • 5)(5 • 5 • 5 • 5)
(5)6 15,625
6•6•6•6• 6 • 6
6•6
662 64 1296
Find the value of each expression. Express answers in standard form.
9. 24
11. 32
10. 60
24 1
1
24 16
60 6
1
6
2 3
14. ( 3 )
13. 62
62 2 2
3 3
17. ( 7 )
2
49
4
1
1
32 9
15. ( 4 )
14
1
44 256
19. ( 5 )
3
(23)
8
27
Lesson 1-5, pages 10–11.
52 16. (3
5)
1
1
53 125
2
1 3
18. ( 2 )
(72)
32 1 4
23
8
33 27
1
1
62 36
12. 53
1
13
1
125
125
53
(3)2
9
(5)2 25
2 4
20. ( 9 )
(2)4
94
16
6561
Chapter 1
9
For More Practice Go To:
Simplify. Express answers in standard form.
22. 52 70 33
36 1 8
37 8
29
25 1 27
24 27
51
25. 27 82 110
27. 4 • 42 32
43
30. 53 • 55 • 56
32(4)6 326
34 81
4 (612) • (342)
33. 62 • 3 2
6 • 3 61 • 32; 1 • 9
6
9 3
6 2
77
77 (2) 75
2
7 49
1 1
25
3 25 • 43
4
1
41. 25 3 1 1
4
•
32 64
1
2048
4
2
42
24
34. 22 • 44 (2 ) • (4 )
2 • 4 22 • 42; 4 • 1
16
3
35. 32
3
5
4
38. 62• 6 3
6 • 6 65 (4)
39. 83 • 11
8
1
81
2
36. 52
5
81; 83 • 81 831
84 4096
3
1
1
51
•
252 51 252
1
1
•
5 625
1
3125
0
10
Chapter 1
42
40. 45 • 12
1 4 2
4 ; 45 • 42
42
452 47 16,384
4
1
1
2
3
46. Maria collected 3 cans on day 1, 6 cans on
day 2, 12 cans on day 3, and 24 cans on day 4.
Let d be the day. Write an expression for the
number of cans she collects on day d. Then
find the number of cans she collects on the
10th day.
3 • 2d1; 3 • 2(10)1 3 • 29 3 • 512 1536;
Maria collects 1536 cans on the 10th day.
47. Which expression below is equivalent to 43 • 4 • 45?
B. 410
52(2) 54
625
3 0 • 3 • 3 2
( 25 ) • ( 25 ) • ( 25 )
(
(4) (4)
4)
43.
44.
5
2
3
2
2
2
3
3 5
3 4
3 1 ( 4 ) • ( 4 ) • ( 4 )
2 1( 5 ) • ( 5 ) • ( 5 )
(5) 5
(4) 4
(
)
(3)
0
2
2
3 0
(5) 5
(4) 4
42. 51 12
25
1
Distance walked per day 3 • n1 , where n the day.
2
3
1
First day 3 • 11 3 • 1 3 ft; second day ft;
2
2
3
3
3
ft;
third day ft; fourth day ft; fifth day 8
16
4
No, the ant will never reach the wall.
410
27 • 25 • 1
675 • 1
675
33(2) 35
243
1
4
1
6
623
60 1
32. 33 • 52 • 60
4•9•8
36 • 8
288
535(6) 58(6)
52 25
45. An ant is 6 feet from a wall. The first day, it
walks half the distance to the wall. Each day,
it walks half the remaining distance to the wall.
How many feet does it walk each of the first
five days? If it walked forever in this pattern,
would it ever reach the wall?
A. 42
63 2 3
216 8
224
32
31. 22 • 32 • 8
61
49 0.064
48.936
28. 6 • 62 23
64 9
73
729 36 1
693 1
694
29. 32 • 34 • 36
24. 72 (0.4)3
512 0.0081
511.9919
26. 93 62 123
128 64 1
64 1
63
2
5
37. 77 • 72
7 • 7 725
23. 83 (0.3)4
4
C. 410
410
D. 4
Copyright © by William H. Sadlier, Inc. All rights reserved.
21. 62 40 23