Name: _________________________________________ Date: ___________________________ Period: ____
TEST #2- REVIEW: EXPONENTS & RADICALS
1. Show all you work on the indicated spaces whenever calculations are necessary.
Remember, no work, no credit.
2. Follow all directions. Read carefully.
3. You will earn bonus points if you earn an A in the review.
4. Each item is tallied individually, including the vocabulary.
5. Test review is due on test day and will not be accepted later.
ID: A
CH 13 Test Review
Define each term in your own words.
1. factor
.
2. prime number
.
3. composite numbe
.
4. prime factorization
.
Write the prime factorization of each number.
5. 18
.
6. 60
.
7. 42
.
1
ID: A
Write the term that best completes each statement.
8. The expression 3 6 is an example of a _____________________ .
9. When 6 is divided by 2, the _____________________ is 3.
10. The expression 5 2 is equivalent to the _____________________ of 5 and 5.
11. The _____________________ in the expression 4 3 is the number 3.
Write each expression as a power.
12. 3  3  3  3  3  3  3
.
13. 2  2  2  2  2
.
14. 5  5  5  5  5  5  23  23]
.
15. 2  2  2  2  37  37
.
Multiply the powers. Show all your work and write your answer as a power.
16. 4 3  4 5
.
17. 2 8  2 3
.
18. 9 3  9
2
ID: A
Divide the powers. Show all your work and write your answer as a power.
19.
28
23
.
20.
47
44
.
21.
17 5
17 4
.
Simplify each expression, if possible. Show all your work and write your answer as a power.
22.
83
38
.
Write each number using a power with a positive exponent.
23. 1,000,000
.
24.
1
1000
.
25.
1
49
.
3
ID: A
Rewrite the power so that the exponent is positive.
26. 8 1
.
27. 5 8
.
28. 6 17
.
Rewrite the fraction so that there is no power in the denominator.
29.
1
24
.
30.
1
20 2
.
31.
1
7
.
Simplify each expression completely. Show all your work.
32. 12 0
.
33. 31 4  31 5
.
34. 2 6  2 3
.
4
ID: A
35.
2 5
20
.
Match each rule with the example that demonstrates it.
a.
b.
c.
d.
e.
22  23  22  3  25
 4  3 4 3
   3
3
3
 
(20 4 ) 5  20
4(5)
 20 20
52
 52  0  52
0
5
(5  3) 4  5 4  3 4
____ 36. power of a power rule
____ 37. product rule of powers
____ 38. power of a product rule
____ 39. quotient rule of powers
____ 40. power of a quotient rule
Rewrite each expression using the power of a power property. (You do not need to evaluate the
expression.)
41. (3 2 ) 2
.
42. (5 7 ) 2
.
43. (17 5 ) 6
.
5
ID: A
Rewrite each expression using the power of a product property. (You do not need to evaluate the
expression.)
44. (2  13) 3
.
45. (4  16) 2
.
46. (17  12) 2
.
Rewrite each expression using the power of a quotient property. (You do not need to evaluate the
expression.)
 3  8
47.  
 5
.
 13  7
48.  
 6 
.
10
 8 
49.  
 27 
.
Simplify each algebraic expression. Show all your work.
50. (y 5 ) 3
.
51. (5a) 3
6
ID: A
52. z 13 z 8
.
 x  5
53.  
8
.
For each problem below, identify the property that is used in each step to simplify the expression.
54.
 4 5  2 
 2
 x x y 


   xy 
 2 3 
 2 3 
 2 y 
2 y 



______________________
power of a product
______________________
(xy) 2
Word Bank
(2 2 y 3 ) 2
product rule of powers
quotient rule of powers
2

x y
2 2
2
______________________
3 2
(2 ) (y )
power of a quotient
power of a power


x2y2
______________________
24 y 6
x2
24 y 4
______________________
55.
5a 6 a 4
5a 10
2

(ab)

 (ab) 2
(a 2 ) 3
(a 2 ) 3
____________________
5a 10
 6  (ab) 2
a
____________________
 5a 4  (ab) 2
____________________
 5a 4  a 2 b 2
____________________
 5a 6 b 2
____________________
7
Word Bank
product rule of powers
product rule of powers
power of a power
power of a product
quotient rule of powers
ID: A
Calculate each product.
7
56.
7
.
11 
57.
11
.
58.
2
18
4
25
.
59.
.
Simplify each radical completely.
8
60.
.
50
61.
.
20
62.
.
112
63.
.
8
ID: A
Calculate each sum or difference.
64. 17 2  6 2
.
65. 32 7  17 7
.
66. 
8 5 2 2 3
.
Simplify each expression completely.
3

4
67.
27
2
.
68.
9 2
50

7
21
.
9
ID: A
CH 13 Test Review
Answer Section
1. ANS:
A factor of a number is a number that evenly divides the given number with no remainder.
PTS: 1
REF: Ch9.L1
STA: A.4.1
TOP: Skills Practice
2. ANS:
A prime number is a whole number greater than 1 that has exactly two whole number factors, 1 and itself.
PTS: 1
REF: Ch9.L1
STA: A.4.1
TOP: Skills Practice
3. ANS:
A composite number is a whole number greater than 1 that is divisible by 1, itself, and at least one other
positive number.
PTS: 1
REF: Ch9.L1
STA: A.4.1
TOP: Skills Practice
4. ANS:
The prime factorization of a number is the representation of the number as a product of prime numbers.
PTS: 1
5. ANS:
18  2  3  3  2  3 2
REF: Ch9.L1
STA: A.4.1
TOP: Skills Practice
PTS: 1
REF: Ch9.L1
6. ANS:
60  2  2  3  5  2 2  3  5
STA: A.4.1
TOP: Skills Practice
PTS: 1
7. ANS:
42  2  3  7
REF: Ch9.L1
STA: A.4.1
TOP: Skills Practice
PTS: 1
8. ANS: power
REF: Ch9.L1
STA: A.4.1
TOP: Skills Practice
PTS: 1
9. ANS: quotient
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
10. ANS: product
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
11. ANS: exponent
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
12. ANS:
37
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
1
ID: A
13. ANS:
25
PTS: 1
14. ANS:
5 6  23 2
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
15. ANS:
2 4  37 2
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
16. ANS:
43  45  43  5  48
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
17. ANS:
2 8  2 3  2 8  3  2 11
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
REF: Ch9.L2
18. ANS:
93  9  93  91  93  1  94
STA: A.4.1
TOP: Skills Practice
PTS: 1
19. ANS:
28
 28  3  25
3
2
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
20. ANS:
47
 47  4  43
4
4
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
REF: Ch9.L2
21. ANS:
17 5
 17 5  4  17 1  17
17 4
STA: A.4.1
TOP: Skills Practice
PTS: 1
22. ANS:
83
 8 ; Not possible
3
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
REF: Ch9.L2
STA: A.4.1
TOP: Skills Practice
PTS: 1
2
ID: A
23. ANS:
10 6
PTS: 1
24. ANS:
1
10 3
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
PTS: 1
25. ANS:
1
72
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
PTS: 1
26. ANS:
1
8
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
PTS: 1
27. ANS:
1
58
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
PTS: 1
28. ANS:
1
6 17
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
PTS: 1
29. ANS:
2 4
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
PTS: 1
30. ANS:
20 2
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
PTS: 1
31. ANS:
7 1
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
PTS: 1
32. ANS:
1
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
PTS: 1
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
3
ID: A
33. ANS:
 31 4  5  31 1  31
PTS: 1
34. ANS:
 26  3  23  8
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
PTS: 1
35. ANS:
REF: Ch9.L3
STA: A.4.1
TOP: Skills Practice
Ch9.L3
1
STA: A.4.1
REF: Ch9.L4
TOP: Skills Practice
STA: A.4.1
1
REF: Ch9.L4
STA: A.4.1
1
REF: Ch9.L4
STA: A.4.1
1
REF: Ch9.L4
STA: A.4.1
1
REF: Ch9.L4
STA: A.4.1
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
PTS: 1
44. ANS:
 2 3  13 3
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
PTS: 1
45. ANS:
 4 2  16 2
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
 2 5  0  2 5 
36.
37.
38.
39.
40.
41.
PTS:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
3
2(2)
1
REF:
C
PTS:
Skills Practice
A
PTS:
Skills Practice
E
PTS:
Skills Practice
D
PTS:
Skills Practice
B
PTS:
Skills Practice
 34
PTS: 1
42. ANS:
5
7(2)
 5 14
PTS: 1
43. ANS:
 17
1
1

5
32
2
5(6)
 17 30
PTS: 1
4
ID: A
46. ANS:
 17 2  12 2
PTS: 1
47. ANS:
38
 8
5
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
PTS: 1
48. ANS:
13 7
 7
6
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
PTS: 1
49. ANS:
8 10
 10
27
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
PTS: 1
50. ANS:
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
PTS: 1
REF: Ch9.L4
51. ANS:
(5a) 3  5 3 a 3  125a 3 5 3 a 3
STA: A.4.1
TOP: Skills Practice
PTS: 1
52. ANS:
z 13 z 8  z 13  8  z 21
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
PTS: 1
53. ANS:
x5
 5
8
REF: Ch9.L4
STA: A.4.1
TOP: Skills Practice
PTS: 1
REF: Ch9.L4
54. ANS:
product rule of powers
STA: A.4.1
TOP: Skills Practice
STA: A.4.1
TOP: Skills Practice
(y 5 ) 3  y
5(3)
 y 15
power of a quotient
power of a product
power of a power
quotient rule of powers
PTS: 1
REF: Ch9.L4
5
ID: A
55. ANS:
product rule of powers
power of a power
quotient rule of powers
power of a product
product rule of powers
PTS: 1
56. ANS:
7 7 7
REF: Ch9.L4
STA: A.4.1
PTS: 1
57. ANS:
11  11  11
REF: Ch9.L5
STA: A.6.1 | A.6.2 TOP: Skills Practice
PTS: 1
58. ANS:
2  18 
REF: Ch9.L5
STA: A.6.1 | A.6.2 TOP: Skills Practice
36  6
PTS: 1
59. ANS:
4  25 
PTS: 1
60. ANS:
8 4
REF: Ch9.L5
REF: Ch9.L5
STA: A.6.1 | A.6.2 TOP: Skills Practice
2 2 2
PTS: 1
62. ANS:
20  4
REF: Ch9.L5
REF: Ch9.L5
STA: A.6.1 | A.6.2 TOP: Skills Practice
5 2 5
REF: Ch9.L5
16
STA: A.6.1 | A.6.2 TOP: Skills Practice
2 5 2
STA: A.6.1 | A.6.2 TOP: Skills Practice
7 4 7
PTS: 1
REF: Ch9.L5
64. ANS:
17 2  6 2  23 2
PTS: 1
STA: A.6.1 | A.6.2 TOP: Skills Practice
100  10
PTS: 1
61. ANS:
50  25
PTS: 1
63. ANS:
112 
TOP: Skills Practice
REF: Ch9.L5
STA: A.6.1 | A.6.2 TOP: Skills Practice
STA: A.6.1 | A.6.2 TOP: Skills Practice
6
ID: A
65. ANS:
32 7  17 7  15 7
PTS: 1
REF: Ch9.L5
STA: A.6.1 | A.6.2 TOP: Skills Practice
66. ANS:
 8 5 2 2 3   4 2 5 2 2 3
 2 2  5 2  2 3  3 2  2 3
PTS: 1
67. ANS:
3

4

REF: Ch9.L5
27
3


2
4
9 3
3 3 3


2
4
2
3 6 3 7 3

4
4
PTS: 1
68. ANS:
REF: Ch9.L5
9 2
50 9 2



7
21
7

STA: A.6.1 | A.6.2 TOP: Skills Practice
STA: A.6.1 | A.6.2 TOP: Skills Practice
25 2
21
9 2 5 2 27 2  5 2 32 2



7
21
21
21
PTS: 1
REF: Ch9.L5
STA: A.6.1 | A.6.2 TOP: Skills Practice
7