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1.1 Evaluate Expressions
Goal  Evaluate algebraic expressions and use exponents.
Your Notes
VOCABULARY
Variable
A letter used to represent one or more numbers
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Algebraic expression
A collection of numbers, variables, and operations
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An algebraic
expression is also
called a variable
expression.
Evaluating an expression
Substituting a number for the variable, performing the operation(s), and simplifying the
result if necessary
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Power
An expression that represents repeated multiplication of the same factor
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Base
The number or expression that is used as a factor in repeated multiplication
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Exponent
A number or expression that represents the number of times the base is used as a factor
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ALGEBRAIC EXPRESSIONS
Algebraic Expression
Meaning
Operation
7t
x
20
7 times t
_Multiplication_
__x divided by 20__
Division
y8
__y minus 8__
__Subtraction__
12  a
__12 plus a__
__Addition__
Your Notes
Example 1
Evaluate algebraic expressions
Evaluate the expression when n = 4.
Substitute _4__ for n.
a. 11  n = 11  _4__
= _44_
__Multiply__.
To evaluate an
expression,
substitute a
number for the
variable,
perform the
operation(s),
and simplify.
12
b.
n

12
4
= __3__
c. n – 3 = __4__  3
= __1__
Substitute __4__ for n.
__Divide__.
Substitute __4__ for n.
__Subtract__.
Checkpoint Evaluate the expression when y = 8.
1. 7y
56
2. y  2
4
3. 10  y
2
4. y + 6
14
Example 2
Read and write powers
Write the power in words and as a product.
Power
Words
Product
a. 121
twelve to the __first__ power
__12__
b. 23
two to the __third__power, or
two __cubed__
__2  2  2__
1
c.  
4
d. a4
2
one fourth to the __second__
power, or one fourth
__squared__
a to the __fourth__ power
1 1

4 4
__a  a  a  a__
Your Notes
Checkpoint Write the power in words and as a product.
5. 75
seven to the fifth power
7  7  7  7 7
2
1
6.  
3
one third to the second power, or one third squared
1 1

3 3
7. (1.4)3
one and four tenths to the third power, or one and four tenths cubed
(1.4) (1.4) (1.4)
Example 3
Evaluate powers
Evaluate the expression.
a. y3 when y = 3
b. a5 when a = 1.2
Solution
a. y3 = _3_3
Substitute __3__ for y.
= _3  3  3_
__Write factors__.
= _27_
__Multiply__.
b. a5 = _1.2_5
Substitute _1.2_ for a.
= __(1.2) (1.2) (1.2) (1.2) (1.2)__
__Write factors__.
= __2.48832__
__Multiply__.
Checkpoint Evaluate the expression.
8. t2 when t = 3
9
9. m5 when
1
m
2
1
32
10. x3 when
x=4
64
Homework
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