Name: _________________
Block: ____________
Date: ______________
Math 6: Study Guide 4
Properties, Exponents, Square Roots,
Sequences, and Order of Operations
Section 1: Properties
Match the following properties with the examples. The answer choices can
be used once, more than once, or not at all. Write your answer on the line
with a CAPITAL letter.
A Identity Property of Addition
B Identity Property of Multiplication
C Multiplicative Property of Zero
D Inverse Property of Multiplication
E Inverse Property of Addition
1.) ________
3·0 = 0
2.) ________
9x + 0 = 9x
3.) ________
4.) ________
5.) _______
5
5
x1=
6
6
6.) ________
4
5
x
=1
5
4
7.) ________
1=9x
45  1= 45
-7 + 7 = 0
1
9
Name: _________________
Block: ____________
Date: ______________
Fill in the blanks with the correct information to make the
property true.
8.)
9.)
10.)
12 = 1  ________
74 (____) = 0
2
X _____ = 1
7
11.) -17 + ____ = 0
12.)
_____ + 0 = .34
Name: _________________
Block: ____________
Date: ______________
Section 2: Exponents
Write each power (exponential form) as a product of factors.
Then evaluate.
13.
Exponential
Form
Product of Factors
Evaluate
35
23
92
10
Write each product of factors in exponential form. Then evaluate.
14.
Exponential
Form
Product of Factors
3×3×3
1×1×1×1
11 × 11
4×4×4×4×4
Evaluate
Name: _________________
Block: ____________
Date: ______________
15. Based on the pattern shown, what is the value of 55?
51 = 5
52 = 25
53 = 125
55 = __________
16. Look at the given example:
33 =
32 =
31 =
30 =
3 × 3 × 3 = 27
3×3=9
3 =3
1
Now explain why 40 = 1 , using pictures, numbers or words.
Name: _________________
Block: ____________
Date: ______________
Section 3: Perfect Squares and Square Roots
17. List the first 12 perfect squares in ascending order.
______ ,
_____ ,
_____ , _____ ,
_____ ,
_____ ,
______ , ______ , _____ , _____ ,
_____ ,
_____
Evaluate:
18. √49
19. √121
20. √9
21.
√81
22. What perfect square is between 121 and 169?
Name: _________________
Block: ____________
Date: ______________
Section 4: Order of Operations (NO CALCULATOR)
Apply order of operations to the following problems. Show each
step clearly.
23.
53 – 32 × 5
24.
(11 – 9)3
25.
36 ÷ 2 × 5
26.
(12 + 49 – 52) × (7 + 0)
Name: _________________
27.
Block: ____________
Date: ______________
(20 – 10 ÷10)2 – 82 + 5
28. Find the mistake in the given problem. Circle the mistake
and explain what went wrong.
(23 – 1 + 3) ÷ 2 + 32
(8 – 1 + 3) ÷ 2 + 32
(8 - 4) ÷ 2 + 32
(4) ÷ 2 + 32
4÷2+9
2+9
11
___________________________________________________
____________________________________________________