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Worksheets05 Nonlinear Expressions Unit Review
Total questions: 60
Worksheet time: 15hrs 0mins
Name
Class
Date
1.
The Product Property states that like factors can be combined by multiplication: The base stays the same and you __________________ the exponents
a)
Add
b)
Subtract
c)
Multiply
d)
Divide
2.
The Quotient Property states that you can combine like factors by division: The base stays the same and you ____________________ the exponents
a)
Subtract
b)
Add
c)
Multiply
d)
Divide
3.
The Distributive Rule for Powers states: "The exponent on the outside ________________ every exponent on the inside - including the hidden 'ones'."
a)
Multiplied by
b)
Added to
c)
Subtracted from
d)
Divided by
4.
The Zero Property of Powers states that any base (except zero) with an exponent of zero equals ___________________________
a)
One
b)
Zero
c)
That base
d)
Infinity
5.
Which of the following equations correctly represents the Inverse Property of Powers? (Assuming x≠0)
a)
x-a = 1/(xa)
b)
x-a = (-x)a
c)
x-a = -xa
d)
x-a = (-a)(1/x)
6.
Evaluate x2 when x= ⁻3 :
a)
9
b)
-9
c)
6
d)
-6
7.
Evaluate 2x2-3x+6 when x= -5 :
a)
71
b)
-29
c)
-59
d)
41
8.
Simplify: x4x2
a)
x6
b)
x8
c)
(2x)6
d)
(2x)8
9.
Assuming that x≠0, simplify: x12/x4
a)
x8
b)
x3
c)
x16
d)
x48
10.
Assuming x≠0, simplify: x-3
a)
1/(x3)
b)
(-x)3
c)
-3/x
d)
x/(-3)
11.
Simplify: x0 (assume that x≠0)
a)
1
b)
0
c)
x
d)
undefined
12.
Simplify: (3x2)3
a)
27x6
b)
9x6
c)
3x6
d)
9x5
13.
Simplify: (10x15)/(2x5). Assume x≠0.
a)
5x10
b)
8x10
c)
5x3
d)
8x3
14.
Assuming x≠0, simplify: (10x6)-2
a)
1/(100x12)
b)
10/(x12)
c)
-20/(x4)
d)
-20/(x12)
15.
A negative base with an even exponent always evaluates to a/an _____________________ number.
a)
Positive
b)
Negative
c)
Even
d)
Odd
16.
A negative base with an odd exponent always evaluates to a/an ___________________ number.
a)
Negative
b)
Positive
c)
Even
d)
Odd
17.
Simplify: (2x3y5)3
a)
8x9y15
b)
6x9y15
c)
2x9y15
d)
8x6y8
18.
There are 10-9 meters per nanometer. How many cubic meters per cubic nanometer?
a)
10-27
b)
10-6
c)
10-12
d)
10-18
19.
Assuming x≠0, simplify: x7/x14
a)
1/(x7)
b)
1/(x2)
c)
x7
d)
x2
20.
Simplify: 5x2⋅2x5
a)
10x7
b)
7x7
c)
7x10
d)
10x10
21.
Powers represent repeated _______________________. (Note: This definition can be extended by analysis of the pattern it forms.)
a)
Multiplication
b)
Addition
c)
Subtraction
d)
Division
22.
True or False: Exponentiation (^) distributes over multiplication and division.
a)
True
b)
False
23.
True or False: Exponentiation (^) distributes over addition and subtraction.
a)
False
b)
True
24.
Which of the following equations correctly represents the Distributive Property of Powers?
a)
(xa⋅yb)c = xac⋅ybc
b)
(xa⋅yb)c = xa+c⋅yb+c
c)
(xa+yb)c = xac+ybc
d)
(xa+yb)c = xa+c⋅yb+c
25.
Any factor that does not appear to have an exponent actually has a "hidden" exponent of _____
a)
1
b)
0
c)
That base
d)
x
26.
A factor is any set of mathematical symbols linked together by ____________________
a)
Exponentiation and Root
b)
Multiply and Divide
c)
Add and Subtract
d)
Logarithms
27.
Evaluate 9-8
a)
1/(43,046,721)
b)
1/(72)
c)
-72
d)
1/(-72)
28.
Evaluate (2/3)5
a)
32/243
b)
32/5
c)
10/15
d)
1/5
29.
Simplify x12x-15
a)
1/(x3)
b)
1/(x180)
c)
x3
d)
(2x)-3
30.
A positive number with a negative exponent (like 5-2) will always evaluate to a ____________________
a)
Positive fraction
b)
Negative fraction
c)
Positive whole number
d)
Negative whole number
31.
Assuming x≠0, simplify: (x2)/(x-2)
a)
x4
b)
0
c)
1
d)
1/(x4)
32.
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
33.
Which of the following expressions is equivalent to 1?
a)
80
b)
08
c)
(8-8)1
d)
80-80
34.
Two variable factors are considered like factors if and only if they have the exact same ________________
a)
Base
b)
Exponent
c)
Coefficient
d)
Term
35.
Simplify: x6⋅x−6 (Assume x=0 )
a)
1
b)
0
c)
x
d)
6
36.
Simplify the expression: (20x²)/(10x⁸) (assume x≠0)
a)
2/x⁶
b)
2x⁴
c)
10/x⁴
d)
10x⁶
37.
What is the GCF (Greatest Common Factor) of the monomials 6x² and 9x³y?
a)
3x²
b)
3x²y
c)
18x³
d)
18x³y
38.
What is the LCM (Least Common Multiple) of the monomials 6x² and 9x³y?
a)
18x³y
b)
3x²
c)
3x²y
d)
18x³
39.
Which of the following expressions represents the product of 3x² and 12x⁴ ?
a)
36x⁶
b)
15x⁶
c)
36x⁸
d)
15x⁸
40.
An expression that consists of only one term is called a/an:
a)
Monomial
b)
Polynomial
c)
Formula
d)
Function
41.
An expression with more than one term is known as a/an:
a)
Polynomial
b)
Monomial
c)
Formula
d)
Function
42.
Factor the polynomial:
x2 + 7x - 30
x2 + 7x - 30
a)
(x + 10)(x - 7)
b)
(x - 10)(x + 3)
c)
(x + 10)(x + 3)
d)
(x + 10)(x - 3)
43.
Factor the polynomial:
k2+7k+10
k2+7k+10
a)
(k+2)(k+5)
b)
(k-2)(k-5)
c)
(k+10)(k+4)
d)
(k+2)(k-5)
44.
Find the product: (2x + 1)(x - 3)
a)
-3x - 3
b)
2x2 + 5x - 3
c)
2x2 - 5x - 3
d)
2x2 - 5x +3
45.
Divide:
(9x2 + 6x) / (3x) (Assume x=0 )
a)
3x + 2
b)
3x2 + 2x
c)
5x2
d)
3x + 6
46.
Divide (6x2+12x) by 3x (Assume x=0 )
a)
2x+4
b)
2+6/3x
c)
2+4/x
d)
3+6/2x
47.
Divide (6x2+12x) by 3x. What is the quotient? (Assume x=0 )
a)
2x+4
b)
2x+3
c)
2+4/x
d)
3x+4
48.
(2ab)3=
a)
8a3b3
b)
2ab3
c)
6a3b3
d)
6ab
49.
Simplify 3-3
a)
-27
b)
-9
c)
-1/9
d)
1/27
50.
Simplify -4x0 (Assume x=0 )
a)
-4x
b)
-4
c)
1
d)
-1
51.
Find the difference. Subtraction is not your friend!!
(3 - 2x + 2x2) - (4x - 5 + 3x2)=
(3 - 2x + 2x2) - (4x - 5 + 3x2)=
a)
x2 + 6x + 8
b)
2x2 + 5x - 7
c)
-x2 -6x + 8
d)
-2x2 + 11x - 4
52.
Simplify:
4 - 3(22 - 5)
Subtraction is not your friend!!
4 - 3(22 - 5)
Subtraction is not your friend!!
a)
-23
b)
7
c)
-37
d)
-17
53.
Evaluate b2 - 4ac for
b = -5, a = -1, and
c = 2
b = -5, a = -1, and
c = 2
a)
33
b)
-17
c)
13
d)
-33
54.
Evaluate the expression using the Quotient Property of Powers. (Assume z≠0)
a)
214 z13
b)
22/z7
c)
214/ z7
d)
22 z7
55.
Simplify:
(7a2)(5a6b)2
(7a2)(5a6b)2
a)
35a14b2
b)
175a12b2
c)
175a14b2
d)
35a14b
56.
Find the GCF (Greatest Common Factor) of
3xy and 15x3y3
3xy and 15x3y3
a)
15x3y3
b)
3x3y3
c)
45x3y3
d)
3xy
57.
Find the LCM (Least Common Multiple) of
3xy and 15x3y3
3xy and 15x3y3
a)
15x3y3
b)
3x3y3
c)
45x3y3
d)
3xy
58.
Find the GCF (Greatest Common Factor) of
5x2y and 15xy2z
5x2y and 15xy2z
a)
15x2y2z
b)
x2yz
c)
5xy
d)
15xyz
59.
Find the LCM (Least Common Multiple) of
5x2y and 15xy2z
5x2y and 15xy2z
a)
15x2y2z
b)
x2yz
c)
5xy
d)
15xyz
60.
Review: Simplify:
(1/3)(21m + 27) =
(1/3)(21m + 27) =
a)
63m + 9
b)
7m + 9
c)
7m + 81
d)
7m + 27
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