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8-CHAPTER 1 TEST 2023-2024

Total questions: 192

Worksheet time: 6hrs 52mins

Name
Class
Date
1.

What is the base in  565^6  ?

a)

6

b)

5

c)

30

d)

0

2.

What is the exponent in  737^3 ?

a)

3

b)

7

c)

21

d)

0

3.

What is another way to say a number is to the 2nd power?

Check all possible answers.

a)

Squared

b)

Cubed

c)

Diced

d)

The power of 2

4.

What is another way to say a number is to the 3rd power?

Check all possible answers.

a)

Squared

b)

Cubed

c)

Triangle

d)

The power of 3

5.

Represent using an exponent.

7 x 7 x 7 x 7 x 7 x 7 x 7 x 7

a)

77

b)

78

c)

87

d)

79

6.

How could 86 be represented?

Check all possible answers.

a)

8 x 6

b)

8 x 8 x 8 x 8 x 8 x 8

c)

6 x 6 x 6 x 6 x 6 x 6 x 6 x 6

d)

262,144

7.

Represent 54 in standard form.

a)

20

b)

625

c)

265

d)

24

8.

Represent 172 in standard form.

a)

269

b)

279

c)

289

d)

299

9.
What is nine cubed in exponential form?
a)
9 x 9 x 9 
b)
93
c)
92
d)
33
10.

Which is equivalent to 7 x 7 x 7 x 7 x 7 x 7 ?

a)

75

b)

76

c)

67

d)

77

11.

What is 431 x 431 x 431 in exponential form?

a)

34313^{431}

b)

4313431^3

c)

431 x 3

d)

3 x 431

12.

What is 16616^6  in expanded form?

a)

6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6

b)

16 x 16 x 16 x 16 x 16 x 16 

c)

16 x 6

d)

6 x 16

13.

What is 78578^5  in expanded form?

a)

78 x 78 x 78 x 78 x 78 

b)

78 x 78 x 78 x 78 x 78 x 78

c)

78 x 5

d)

5 x 78

14.

Which is least? 123  or  5612^3\ \ or\ \ 5^6  

a)

12312^3  

b)

565^6  

c)

Neither

15.
Which is GREATER?
27 or 72
a)
27
b)
72
c)
Neither, they are equal
16.

Which represents the exponential form of a number?

a)

13x13x13x13x13

b)

135

c)

371,293

17.

Which represents the expanded form of a number?

a)

13x13x13x13x13

b)

135

c)

371,293

18.

Which represents the standard form of a number?

a)

13x13x13x13x13

b)

135

c)

371,293

19.

152 + 233

a)

79,235,168

b)

12,197

c)

12,392

d)

99

20.

97 - 433

a)

4,703,462

b)

66

c)

543

d)

3,214,467

21.
Which is equivalent to 7 x 7 x 7 x 7 x 7 x 7 
?
a)
75
b)
76
c)
67
d)
77
22.
Find the equivalent expression.

9 x 9 x 9 x 9 x 9
a)
95
b)
915
c)
9 x 5
d)
9 + 9 + 9 + 9+ 9
23.
What is the power to this problem?
6 x 6 x 6 x 6 x 6 x 6 x 6
a)
6 to the 7th power
b)
6 to the 8th power
c)
7 to the 9th power
d)
10 to the 5th power
24.
25 is the same as 2 x 5.
a)
True
b)
False
25.
How would you represent 8⁶ ?
a)
8 x 6
b)
8 x 8 x 6
c)
8 x 8 x 8 x 8 x 8 x 8
d)
6 x 6 x 6 x 6 x 6 x 6 x 6 x 6
26.
The exponent equivalent of 20 x 20 x 20 is
a)
20 x 3
b)
203
c)
320
27.
Which is equivalent to 5 x 5 x 5 x 5
a)
53
b)
54
c)
45
d)
55
28.
Which is equivalent to 4 x 4 x 4 x 4 x 4
a)
46
b)
54
c)
44
d)
45
29.

Which is equivalent to 7 x 7 x 7 x 7 x 7

a)

75

b)

76

c)

67

d)

77

30.
How do you correctly say 43
a)
4 squared
b)
3 quadrupled
c)
4 cubed
d)
4 to the power of 2
31.
Find the equivalent expression.
15×15×15×15
a)
154
b)
415
c)
15x4
d)
15+15+15+15
32.

Find the equivalent expression.


9 x 9 x 9

a)

93

b)

915

c)

9 x 5

d)

9 + 9 + 9 + 9+ 9

33.
What is the number in a power that tells how many times the base is used as a factor?
a)
Expression
b)
Exponent
c)
Factor
d)
Term
34.

In the exponent 34, the 3 represents____________ ?

a)

power

b)

base

c)

exponent

d)

integers

35.

What is the power to this problem?

6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6

a)

9 to the 7th power

b)

6 to the 8th power

c)

6 to the 9th power

d)

10 to the 5th power

36.
25 is the same as 2 x 5.
a)
True
b)
False
37.

Write each product using an exponent.

4 x 4

a)

42

b)

54

c)

46

d)

46

38.
How would you represent 8⁶ ?
a)
8 x 6
b)
8 x 8 x 6
c)
8 x 8 x 8 x 8 x 8 x 8
d)
6 x 6 x 6 x 6 x 6 x 6 x 6 x 6
39.
What special word do you use for the exponent of 2?
a)
squared
b)
cubed
c)
triangled
d)
boxed
40.
Which is equivalent to
7 x 7 x 7 x 7 x 7 x 7 ?
a)
75
b)
76
c)
67
d)
77
41.
90
a)
0
b)
1
c)
9
d)
90
42.
34
a)
27
b)
63
c)
72
d)
81
43.
33
a)
6
b)
9
c)
27
d)
54
44.
What is equivalent to 52?
a)
25
b)
10
c)
55
d)
30
45.
What special word do you use for the exponent of 2?
a)
squared
b)
cubed
c)
triangled
d)
boxed
46.
What operation do you use with exponents?
a)
addition
b)
subtraction
c)
multiplication
d)
division
47.
What is the exponential form of 
4 x 4 x 4 x 4 x 4 x 4?
a)
64
b)
42
c)
46
d)
4 x 6
48.
How would you represent 8⁶ ?
a)
8 x 6
b)
8 x 8 x 6
c)
8 x 8 x 8 x 8 x 8 x 8
d)
6 x 6 x 6 x 6 x 6 x 6 x 6 x 6
49.
Which is the expanded form of 
53?
a)
3 x 3 x 3
b)
5 x 5
c)
5 x 5 x 5
d)
5 x 3
50.
What is equivalent to 5 squared?
a)
25
b)
10
c)
55
d)
30
51.
How do you correctly say 43?
a)
4 squared
b)
3 quadrupled
c)
4 cubed
d)
4 to the power of 2
52.
Any number to the zero power is equal to 
a)
0
b)
1
53.
a2 means
a)
a+a
b)
2a
c)
2+a
d)
a×a
54.
bmeans
a)
5b
b)
b×b×b×b×b
c)
5+b
d)
b+b+b+b+b
55.
Evaluate 133
a)
0
b)
1
c)
33
d)
34
56.

(4)2\left(-4\right)^2  

a)

16

b)

-16

c)

-8

d)

8

57.

(5)3\left(-5\right)^3  

a)

125

b)

-125

c)

-15

d)

15

58.

52-5^2  

a)

25

b)

-25

c)

-10

d)

10

59.

(4)4\left(-4\right)^4  

a)

256

b)

-256

c)

-16

d)

16

60.

63-6^3  

a)

216-216  

b)

216216  

c)

18-18  

d)

1818  

61.

(4)5\left(-4\right)^5  

a)

1,024-1,024  

b)

1,0241,024  

c)

20-20  

d)

2020  

62.

(2)6\left(-2\right)^6  

a)

64-64  

b)

6464  

c)

12-12  

d)

1212  

63.

62-6^2  

a)

36-36  

b)

3636  

c)

12-12  

d)

1212  

64.

404^0  

a)

11  

b)

00  

c)

44  

65.

808^0  

a)

11  

b)

00  

c)

88  

66.

For -33 I need to enter (-3)3 in the calculator.

a)

True

b)

False

67.
Are these two equivalent: (-2)3 = 23
a)
Yes
b)
No
68.
03 = ?
a)
1
b)
0
c)
2
69.
50 = ?
a)
1
b)
5
c)
0
d)
50
70.
Evaluate: (-1)2016
a)
-1
b)
-2016
c)
1
d)
2016
71.
Evaluate: (-1)2015
a)
-1
b)
1
c)
-2015
d)
2015
72.

Evaluate:

62-6^2  



(a)  

73.

Evaluate:

23-2^3  



(a)  

74.

525^2   simplified to

a)

10

b)

25

c)

-10

d)

-25

75.

42-4^2   simplifies to

a)

8

b)

-8

c)

-16

d)

16

76.

(2)3\left(-2\right)^3   simplifies to

a)

-8

b)

-6

c)

8

d)

6

77.

23-2^3   simplifies to

a)

-6

b)

-8

c)

6

d)

8

78.

(1)2\left(-1\right)^2   simplifies to

a)

2

b)

1

c)

-2

d)

-1

79.

12-1^2   simplifies to

a)

1

b)

-1

c)

2

d)

-2

80.

(3)2\left(-3\right)^2   simplifies to

a)

-9

b)

9

c)

6

d)

-6

81.
(1/2)2
a)
1/4
b)
1
c)
1/2
d)
1/8
82.
(1/5)2
a)
1/10
b)
2/10
c)
2/25
d)
1/25
83.
(1/3)3
a)
1/27
b)
1/9
c)
1/6
d)
1/3
84.
Challenge #2     (2/3)2
a)
2/6
b)
2/9
c)
4/6
d)
4/9
85.
a)

6/8

b)

9/8

c)

6/16

d)

9/16

86.
a)

1/8

b)

1/6

c)

3/6

d)

3/8

87.
a)

8/18

b)

16/81

c)

16/18

d)

8/81

88.
a)

20/22

b)

100/22

c)

20/121

d)

100/121

89.
a)
1/6
b)
1/36
c)
2/12
d)
1/12
90.

(34)2\left(\frac{3}{4}\right)^2

a)

34\frac{3}{4}  

b)

68\frac{6}{8}  

c)

916\frac{9}{16}  

d)

3040\frac{30}{40}  

91.

Rewrite using a positive exponent.

7107^{-10}  

a)

1710\frac{1}{7^{10}}  

b)

7107^{10}  

c)

1710\frac{1}{7^{-10}}  

d)

70-70  

92.

Rewrite using a positive exponent.

g7g^{-7}  


a)

1g7\frac{1}{g^7}  

b)

g7g^7  

c)

1g7\frac{1}{g^{-7}}  

d)

g7-g^7  

93.

Rewrite using a positive exponent.

w13w^{-13}  


a)

w13-w^{13}  

b)

1w13\frac{1}{w^{13}}  

c)

1w13-\frac{1}{w^{13}}  

d)

1w13\frac{1}{w^{-13}}  

94.

Rewrite the expression with a negative exponent.

1124\frac{1}{12^4}  


a)

1124\frac{1}{12^{-4}}  

b)

12412^4  

c)

120,736\frac{1}{20,736}  

d)

12412^{-4}  

95.

Rewrite the expression with a negative exponent.

1(5)7\frac{1}{\left(-5\right)^7}  


a)

(5)7\left(-5\right)^7  

b)

1(5)7\frac{1}{\left(-5\right)^{-7}}  

c)

(5)7\left(-5\right)^{-7}  

d)

None of the above

96.

Simplify the expression using positive exponents.


1a2\frac{1}{a^{-2}}  

a)

a2a^{-2}  

b)

a2a^2  

c)

1a2\frac{1}{a^2}

d)

None of the above

97.

Evaluate.

525^{-2}  


a)

10-10  

b)

125\frac{1}{25}  

c)

152\frac{1}{5^2}  

d)

15\frac{1}{5}  

98.

Evaluate.


212^{-1}  


a)

12\frac{1}{2}  

b)

11  

c)

2-2  

d)

12-\frac{1}{2}  

99.
Rewrite using a positive exponent.
7-10
a)
1/710
b)
710
c)
1/7-10
d)
-70
100.

Write this expression using positive exponent:

x-7

a)

-7

b)

-7x

c)

1/x7

d)

-1/x7

101.
Rewrite each expression with a negative exponent.
1/124
a)
1/12-4
b)
124
c)
1/20,736
d)
12-4
102.

Simplify

x⁻⁶

a)

1x6\frac{1}{x^6}

b)

x⁶

c)

-x⁶

d)

1x6\frac{-1}{x^6}

103.

Rewrite using a positive exponent.

g-7

a)

1g7\frac{1}{g^7}

b)

g7g^7

c)

1g7\frac{1}{g^{-7}}

104.

Write with positive exponents:

a)

a-2

b)

a2

c)

1a2\frac{1}{a^2}


105.
Rewrite using a positive exponent.
g-7
a)
1/g7
b)
g7
c)
1/g-7
d)
-g7
106.

Simplify


(a)  
Choose from the below words

116\frac{1}{16}  

-16
16
107.

Simplify

a)

127-\frac{1}{27}

b)

127\frac{1}{27}

c)

19\frac{1}{9}

d)

19-\frac{1}{9}

108.

Simplify (32)0=\left(-32\right)^0=

109.

Rewrite using positive exponent

110.

Simplify

a)

-27

b)

127\frac{1}{27}  

c)

-9

d)

19\frac{1}{9}  

111.
Which is greater,  26540 or 50?
(a)  
Choose from the below words
They are the same
26540
50
112.

Solve 5-2 == (a)  

Choose from the below words

125\frac{1}{25}  

-10
 
-25
113.

Simplify (-9)0 ==

114.
Rewrite using a positive exponent.
7-10
a)

1710\frac{1}{7^{10}}  

b)
710
c)

1710\frac{1}{7^{-10}}  

d)
-70
115.

Simplify and make the exponent positive

x-7 ==

116.

Make this negative exponent positive. 9-3 ==

117.
Simplify (-9)0

a)
-9
b)
-1
c)
1
d)
9
118.

Simplify y0 ==

119.

Rewrite using a positive exponent.

y-13

120.

According to exponent rules, when we multiply terms with the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

121.

According to exponent rules, when we divide the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

122.
m ⋅ m⋅ m6
a)
m30
b)
m12
c)
12m
d)
mm11
123.

Simplify the expression.

(x4 )(x12)

a)

x3

b)

x48

c)

x16

d)

x8

124.
Simplify the following:
(x2y)5
a)
x7y5
b)
x2y5
c)
x10y5
d)
x5y5
125.
Simplify.
a)
y15
b)
y5
c)
y2
d)
2y5
126.
m ⋅ m⋅ m6
a)
m30
b)
m12
c)
12m
d)
mm11
127.

(x8) . (x5)

a)

x-40

b)

x-13

c)

x3

d)

x13

128.

x9x7x10x^9\cdot x^{-7}\cdot x^{-10}  

a)

x8x^8  

b)

1x8\frac{1}{x^8}  

c)

x26x^{26}  

d)

1x26\frac{1}{x^{26}}  

129.

y4y4y^4\cdot y^{-4}  

a)

11  

b)

00  

c)

y8y^8  

d)

y16y^{16}  

130.
Evaluate this expression using the quotient rule.
a)
95
b)
99
c)
15
d)
9-5
131.
a)
9
b)
1
c)
27
d)
0
132.
a)
m4
b)
m6
c)
m10
d)
1/m6
133.
a)
5^29
b)
5^-5
c)
5^-12
d)
5^17
134.
Evaluate the expression using the quotient rule.
a)
c7
b)
c-7
c)
c17
d)
c60
135.
Evaluate the expression using the quotient rule.
a)
122
b)
130
c)
622
d)
630
136.
 Evaluate the expression using the quotient rule.
a)
76
b)
7-5
c)
1/75
d)
75
137.
According to exponent rules, when we raise a power to another exponent we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
138.

(88382)2\left(8\cdot8^3\cdot8^2\right)^2  

a)

8108^{10}  

b)

8128^{12}  

c)

898^9  

d)

868^6  

139.
Simplify: (4x5)2
a)
16x10
b)
8x10
c)
16x7
d)
8x7
140.

Simplify the expression. (3n3)5\left(3n^3\right)^5  

a)

243n15243n^{15}  

b)

81n1581n^{15}  

c)

3n153n^{15}  

d)

15n1515n^{15}  

141.
Simplify:
(2x3y)6
a)
2x18y6
b)
64x18y6
c)
64x3y6
d)
2x3y6
142.

Simplify: (x2y3)3

a)

x6y9

b)

x5y6

c)

x1

d)

x6y6

143.

Simplify:

(5ab2)2

a)

25a2b4

b)

10a2b4

c)

5a2b4

d)

25ab2

144.
(r4)6
a)
10r
b)
r10
c)
24r
d)
r24
145.
Simplify: (3x2)3
a)
27x6
b)
9x6
c)
3x6
d)
9x5
146.
Which of the following expressions is equivalent to (2x)3 ?
a)
(2x)(2x)(2x)
b)
2(x)(x)(x)
c)
2x + 2x + 2x
d)
2x⋅3
147.

Simplify (2x4y7)3

a)

6x7y10

b)

6xy32

c)

8x12y21

148.

Simplify the following expression:


(3x3y5)4

a)

3x12y20

b)

81x12y20

c)

12x12y20

d)

81x7y9

149.

Simplify x11x11\frac{x^{11}}{x^{11}}

150.
a)

x11

b)

x18

c)

x7y

d)

x7

151.
a)

x11

b)

x18

c)

x7y

d)

x7

152.

18x102x3\frac{18x^{10}}{2x^3}  

a)

9x79x^7  

b)

9x139x^{13}  

c)

18x718x^7  

d)

2x132x^{13}  

153.
a)
-6c5
b)
-6c
c)
6c
d)
-6c6
154.
Anything raised to a power of zero is always: 
a)
0
b)
1
c)
itself
d)
negative
155.

6m0p02n0p0= ?\frac{6m^0p^0}{2n^0p^0}=\ ?  

a)

6m0p02n0p0= 0\frac{6m^0p^0}{2n^0p^0}=\ 0  

b)

6m0p02n0p0= 1\frac{6m^0p^0}{2n^0p^0}=\ 1  

c)

6m0p02n0p0= 3\frac{6m^0p^0}{2n^0p^0}=\ 3  

d)

6m0p02n0p0= 3\frac{6m^0p^0}{2n^0p^0}=\ -3  

156.
a)

w-3

b)

w3

c)

w2

d)

w-13

157.
a)
4y6
b)
4y22
c)
30y6
d)
30y22
158.
a)
58
b)
56
c)
52
d)
1
159.
a)
x25
b)
x5
c)
x144
d)
25x
160.
a)
x15
b)
6x13
c)
2x56
d)
x19
161.
Simplify (-4r5)(2r8)
a)
-8r13
b)
-2r13
c)
-8r40
d)
-2y40
162.
Evaluate using the quotient rule: 
a)
a8b13
b)
a2b7
c)
a15b30
163.

Simplify using exponent rules.

a)

32x3y4

b)

32x9y13

c)

16x8y12

d)

16x6y7

164.
Simplify.
a)
y15
b)
y5
c)
y2
d)
2y5
165.
a)
2a4b4
b)
4a3b4
c)
4a8b5
d)
2a4b3
166.
Simplify the exponential expression:
a)
10x-2
b)
2x2
c)
2x12
d)
10x12
167.
a)
3x3
b)
-4x7
c)
-3x7
d)
-3x3
168.
a)
2a2b6
b)
1/2a2b6
c)
b6/2a2
d)
2b6/a2
169.
a)
49
b)
444
c)
421
d)
415
170.
(-6xy3)(x4y2)
a)
-6x5y5
b)
-6x4y5
c)
6x5y5
d)
6x4y6
171.
simplify (5x3 )(2x2)
a)
10x5
b)
3x
c)
10x6
d)
7x5
172.
Simplify (-4r5)(2r8)
a)
-8r13
b)
-2r13
c)
-8r40
d)
-2y40
173.

Simplify: 4x4 × 5x3 =4x^4\ \times\ 5x^{-3}\ =

a)

20x720x^7

b)

20x-20x

c)

20x720x^7

d)

20x20x

174.

Simplify: 16x44x2\frac{16x^4}{4x^2}

a)

12x612x^6

b)

4x24x^2

c)

4x64x^6

d)

12x212x^2

175.

Simplify: (2x6) (3x3)\left(-2x^6\right)\ \left(-3x^{-3}\right)

a)

6x9-6x^{-9}

b)

6x96x^9

c)

6x36x^3

d)

6x3-6x^3

176.

Simplify: 27x89x2\frac{-27x^8}{9x^2}

a)

3x103x^{10}

b)

3x10-3x^{10}

c)

3x63x^6

d)

3x6-3x^6

177.

Simplify: a2b3 × a2b2a^2b^{3\ }\times\ a^2b^{-2}

a)

a4ba^4b

b)

a4b5a^4b^5

c)

a3b6a^3b^6

d)

a4b6a^4b^{-6}

178.

Simplify: z2 × z2z^2\ \times\ z^{-2}

a)

z4z^{-4}

b)

1

c)

z4z^4

d)

z1z^1

179.

Simplify: a0a^0

a)

a1a^1

b)

nothing

c)

1

d)

a1a^{-1}

180.

Simplify: 32a2b54a2b3\frac{32a^2b^5}{-4a^2b^3}

a)

8b88b^8

b)

8b8-8b^8

c)

8b28b^2

d)

8b2-8b^2

181.

Simplify: 45a95a4\frac{-45a^9}{-5a^4}

a)

9a13-9a^{13}

b)

9a59a^5

c)

9a5-9a^5

d)

9a139a^{13}

182.

Simplify: 18a29b2\frac{18a^2}{9b^2}

a)

2ab42ab^4

b)

22

c)

2a2b2\frac{2a^2}{b^2}

d)

2a2b22a^2b^2

183.

Simplify: (8x5) (2x4)\left(8x^5\right)\ \left(-2x^{-4}\right)

a)

16x16x

b)

16x20-16x^{-20}

c)

16x-16x^{ }

d)

16x9-16x^{-9}

184.

Simplify: 34 × 353^4\ \times\ 3^5

a)

9209^{20}

b)

999^9

c)

393^9

d)

3203^{20}

185.

Simplify: 5553\frac{5^5}{5^3}

a)

525^2

b)

535^3

c)

5155^{15}

d)

5205^{20}

186.

Simplify: (6r) (2r3)\left(6r\right)\ \left(2r^3\right)

a)

10r410r^4

b)

12r312r^3

c)

10r310r^3

d)

12r412r^4

187.

Simplify: 2v2 × 4v4 ×v2v^2\ \times\ 4v^4\ \times v^{ }

a)

8v68v^6

b)

8v78v^7

c)

6v76v^7

d)

6v66v^6

188.

Simplify: 10a22a4\frac{-10a^2}{-2a^4}

a)

5a25a^2

b)

5a2-5a^2

c)

5a2\frac{5}{a^2}

d)

5a2\frac{-5}{a^2}

189.

Simplify: 16a48a4\frac{16a^4}{8a^4}

a)

2a8\frac{2}{a^8}

b)

2a82a^8

c)

2-2

d)

22

190.

Simplify: a2c4 × a4c6a^2c^4\ \times\ a^4c^{-6}

a)

a6c2a^6c^2

b)

a6c2\frac{a^6}{c^2}

c)

a8c2a^8c^2

d)

a8c24\frac{a^8}{c^{24}}

191.

Simplify: a4b8a3b7\frac{a^4b^8}{a^3b^7}

a)

abab

b)

a2b2a^2b^2

c)

a7b15a^7b^{15}

d)

a4b2a^4b^2

192.

Simplify: 15t2m33t2m\frac{15t^2m^3}{3t^2m}

a)

5t25t^2

b)

5tm5tm

c)

5tm25tm^2

d)

5m25m^2