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1.1 Evaluate Expressions
You will evaluate algebraic expressions and use exponents
Essential Question: How do you evaluate algebraic expressions and powers?
Warm-Up Exercises
Substitute 3 for n.Multiply.= 39
Subtract.= 2Substitute 3 for n.
Substitute 3 for n.
= 3 Divide.
EXAMPLE 1 Evaluate algebraic expressions
Evaluate the expression when n = 3.
a. 13 n = 13 3
93
b. 9n
=
c. n – 1 =
Substitute 3 for n.
Add.= 11 d. n + 8 =
3 – 1
3 + 8
Warm-Up ExercisesGUIDED PRACTICE for Example 1
= 12
= 6
= 4
Evaluate the expression when y = 2.
1. 6y
2. 8y
3. y + 4
= 9 4. 11 – y
Warm-Up ExercisesEXAMPLE 2 Evaluate an expression
Movies
The total cost of seeing a movie at a theater can be represented by the expression a + r where a is the cost (in dollars) of admission and r is the cost (in dollars) of refreshments. Suppose you pay $7.50 for admission and $7.25 for refreshments. Find the total cost.
Warm-Up Exercises
Add.
The total cost is $14.75
ANSWER
Substitute 7.50 for a and 7.25 for r.
= 14.75
= 7.50 + 7.25
Write expression.Total cost =
EXAMPLE 2 Evaluate an expression
SOLUTION
a + r
Warm-Up Exercises
ProductWordsPower
EXAMPLE 3 Read and write powers
Write the power in words and as a product.
seven to the first powera. 71 7
five to the second power,or five squared
b. 52 5 5
c. 1 3 2
one half to the third power,or one half cubed
12
12
12
z to the fifth powerd. z5 z z z z z
Warm-Up ExercisesGUIDED PRACTICE for Examples 2 and 3
5. WHAT IF? In Example 2, suppose you go back to the theater with a friend to see an afternoon movie. You pay for both admissions.Your total cost (in dollars) can be represented by the expression 2a. If each admission costs $4.75, what is your total cost?
The total cost is $9.50.
ANSWER
Warm-Up ExercisesGUIDED PRACTICE for Examples 2 and 3
ProductWordsPower
Write the power in words and as a product.
Nine to the fifth power6. 95
Two to the eighth power7. 28
n to the fourth power
9 9 9 9 9
2 2 2 2 2 2 2 2
8. n4 n n n n
Warm-Up ExercisesEXAMPLE 4 Evaluate powers
Evaluate the expression.
a. x4 = 24
= 16= (1.5)(1.5)(1.5)= 3.375
= 2 2 2 2b. n3 = 1.53
b. n3 when n = 1.5
SOLUTION
a. x4 when x = 2
Warm-Up ExercisesGUIDED PRACTICE for Example 4
Evaluate the expression.
9. x3 when x = 8
9. 512 10. 6.25
10. k3 when k = 2.5
ANSWER
Warm-Up ExercisesGUIDED PRACTICE for Example 4
Evaluate the expression.
11. d4 when d = 13
11. 181
ANSWER
Warm-Up Exercises
SOLUTION
EXAMPLE 5 Evaluate a power
Storage cubes
Write formula for volume.
= 143 Substitute 14 for s.
= 2744 Evaluate power.
Each edge of the medium-sized pop-up storage cube shown is 14 inches long. The storage cube is made so that it can be folded flat when not in use. Find the volume of the storage cube.
V = s3
The volume of the storage cube is 2744 cubic inches.
Warm-Up ExercisesGUIDED PRACTICE for Example 5
WHAT IF? In Example 5, suppose the storage cube is folded flat to form a square. Find the area of the square.
The area of the square is 196 in2.
ANSWER
Warm-Up ExercisesDaily Homework Quiz
3. 54
ANSWER 0.9
ANSWER 625
2. 1.65 – a when a = 0.75
Evaluate the expression or power.
1. 13g when g = 7
ANSWER 91
Warm-Up ExercisesDaily Homework Quiz
13
34.
Emily is saving for a $300 bicycle. She has saved $128.25. The amount she still needs to save is given by the expression c – s, where c is the cost of the bicycle and s is the amount she has saved. How much does she have left to save?
5.
$171.75 ANSWER
ANSWER 127
You will evaluate algebraic expressions and use exponents
Essential Question: How do you evaluate algebraic expressions and powers?
Algebraic expressions can be used to represent a situation in which the actual numerical value used may change.
A power is written using a base and an exponent. The exponent is the number of times you multiply the base by itself
To evaluate an algebraic expression, substitute the given value for the variable and then perform the operation. To evaluate a power, multiply the base by itself the number of times indicated by the exponent.
