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Study Guide and Review
Determine whether each statement is true or false . If false , replace the underlined word or number to
make a true statement.
The exponent of a number raised to the first power can be omitted.
An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first
power can be omitted. The statement is true.
A number is in scientific notation when it does not contain exponents.
A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the
statement is false. A number is in standard form when it does not contain exponents.
7
In 5 , the number 7 is the base.
7
The number that is multiplied is called the base. So, the statement is false. In 5 , the number 7 is the exponent.
The number 49 is an example of a(n) prime number.
A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The
number 49 is an example of a composite number.
x
The equation y = 5 + 2 is an example of a(n) exponential function.
x
An exponential function is a function that can be described by an equation of the form y = a + c, where a
a
The graph of a(n) cubic function is called a parabola.
The statement is false. The graph of a quadratic function is called a parabola.
To multiply powers with the same base, add the exponents.
The statement is true.
A(n) nonlinear function has a constant rate of change.
Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a
constant rate of change.
6 5
To simplify (n ) , the first step is to add 6 and 5.
6 5
To find the power of a power, multiply exponents. So, the statement is false. To simplify (n ) , the first step is to
multiply 6 and 5.
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The graph of a(n) quadratic function is symmetric.
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A(n) nonlinear function has a constant rate of change.
Nonlinear
do not have constant rates of change. So, the statement is false. A linear function
Study
Guidefunctions
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has a
constant rate of change.
6 5
To simplify (n ) , the first step is to add 6 and 5.
6 5
To find the power of a power, multiply exponents. So, the statement is false. To simplify (n ) , the first step is to
multiply 6 and 5.
The graph of a(n) quadratic function is symmetric.
The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.
Write each expression using exponents.
6 6 6 6 6
The base 6 is a factor 5 times. So, the exponent is 5.
5
6 6 6 6 6=6
4
The base 4 is a factor 1 time. So, the exponent is 1.
1
4=4
x x x
The base x is a factor 3 times. So the exponent is 3.
x x x=x
f f
3
g g g g
Evaluate each expression.
5
3
3
2 4
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Evaluate
expression
x
2
6
w=
, x = 4, y = 1, and z = 5.
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Study Guide and Review
Evaluate each expression if w =
x
2
, x = 4, y = 1, and z = 5.
3
6
w +y
2
3
2(y + z )
4 2
w x yz
TEETH Adult humans have 25 teeth. How many teeth do adults have?
So, adult humans have 32 teeth.
Write the prime factorization of each number. Use exponents for repeated factors.
34
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34 = 2 17
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Study Guide and Review
So, adult humans have 32 teeth.
Write the prime factorization of each number. Use exponents for repeated factors.
34
34 = 2 17
40
63
225
Factor each monomial.
18x
18x = 2 3 3 x
10r
2
32pq
32pq = 2 2 2 2 2 p
q
2
25ab
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PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers
of rows and columns can she display them if each row has the same number of photographs? Name each
arrangement.
32pq
Study Guide and Review
32pq = 2 2 2 2 2 p
q
2
25ab
PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers
of rows and columns can she display them if each row has the same number of photographs? Name each
arrangement.
List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the
following number of rows and columns: 1 24, 24 1, 2 12, 12 2, 3 8, 8 3, 4 6, 6 4. There are 8 different
arrangements.
Find each product or quotient. Express using exponents.
5
2
3
3
4
( 7) ( 7)
3
6
m
x
m
8
x
7
(2h )(6h)
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3
4
(5a )( 6a )
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x
x
Study Guide and Review
7
(2h )(6h)
3
4
(5a )( 6a )
8
9
PLANETS Venus is about 10 kilometers from the Sun. Saturn is about 10 kilometers from the Sun. About how
many times farther from the Sun is Saturn than Venus?
To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by the
distance Venus is from the Sun.
So, Saturn is about 10 times further from the Sun than Venus.
Write each expression using a positive exponent.
4
9
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9
=
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distance Venus is from the Sun.
Study Guide and Review
So, Saturn is about 10 times further from the Sun than Venus.
Write each expression using a positive exponent.
4
9
9
4
=
( 10)
2
( 10)
2
m
m
=
5
5
=
Write each fraction as an expression using a negative exponent other than 1.
=6
3
or
3
MEASUREMENT If 1 millimeter is equal to 10 meter and 1 nanometer is equal to 10
nanometers are in 1 millimeter? Write using a positive exponent.
9
meter, how many
To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of
nanometers in a meter.
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Study Guide and Review
3
MEASUREMENT If 1 millimeter is equal to 10 meter and 1 nanometer is equal to 10
nanometers are in 1 millimeter? Write using a positive exponent.
9
meter, how many
To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of
nanometers in a meter.
6
So, there are 10 nanometers in 1 millimeter.
Express each number in standard form.
3
2
4
5
Express each number in scientific notation.
379
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26,880
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Study Guide and Review
Express each number in scientific notation.
379
26,880
0.0014
0.000561
SPACE
15
exagrams. Express in standard form.
So, the mass of the Sun is 1,988,920,000,000,000 exagrams.
Simplify.
6 3
(2 )
2 8
(r )
7 2
(3x )
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Study Guide and Review
7 2
(3x )
4 6
( 2n )
9
(4a b)
4
5 8 3
(5w x )
GEOMETRY Find the area of the square shown below.
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