1. 1.1 Evaluate Expressions
You will evaluate algebraic expressions and use exponents
Essential Question: How do you evaluate algebraic expressions and
powers?

2. Evaluate algebraic expressions
EXAMPLE 1
Evaluate algebraic expressions
Evaluate the expression when n = 3.
a n =
13 3
Substitute 3 for n.
= 39
Multiply. b. 9 n 9 3 =
Substitute 3 for n.
= 3
Divide.
c. n – 1 =
3 – 1
Substitute 3 for n.
= 2
Subtract.
d. n =
3 + 8
Substitute 3 for n.
= 11
Add. 2

3. Evaluate the expression when y = 2.
GUIDED PRACTICE
for Example 1
Evaluate the expression when y = 2.
1. 6y
= 12 2. 8 y
= 4
3. y + 4
= 6
– y
= 9 3

4. EXAMPLE 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.

5. Evaluate an expression
EXAMPLE 2
Evaluate an expression
SOLUTION
Total cost =
a + r
Write expression. =
Substitute 7.50 for a and
7.25 for r. =
Add.
The total cost is $14.75
ANSWER

6. EXAMPLE 3
Read and write powers
Write the power in words and as a product.
Product
Words
Power a
seven to the first power 7 b
five to the second power,
or five squared
5 5 c.
1 3 2 1 2
one half to the third power, or one half cubed
d. z5
z to the fifth power
z z z z z

7. GUIDED 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

8. GUIDED PRACTICE
for Examples 2 and 3
Write the power in words and as a product.
Product
Words
Power
Nine to the fifth power
Two to the eighth power 8. n4
n to the fourth power
n n n n

9. EXAMPLE 4
Evaluate powers
Evaluate the expression.
a. x4 when x = 2
b. n3 when n = 1.5
SOLUTION
a. x4 = 24
b. n3 = 1.53 =
= (1.5)(1.5)(1.5)
= 16 =

10. GUIDED PRACTICE
for Example 4
Evaluate the expression.
9. x3 when x = 8
k3 when k = 2.5
ANSWER

11. GUIDED PRACTICE
for Example 4
Evaluate the expression.
d4 when d = 1 3
ANSWER
11. 1 81

12. The volume of the storage cube is 2744 cubic inches.
EXAMPLE 5
Evaluate a power
Storage cubes
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.
SOLUTION
V = s3
Write formula for volume.
= 143
Substitute 14 for s.
= 2744
Evaluate power.
The volume of the storage cube is 2744 cubic inches. 12

13. The area of the square is 196 in2. ANSWER
GUIDED 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 13

14. Evaluate the expression or power.
Daily Homework Quiz
Evaluate the expression or power.
g when g = 7
ANSWER 91
– a when a = 0.75
ANSWER
0.9
ANSWER
625 14

15. Daily Homework Quiz 1 4. 3 1 ANSWER 27 5.
Emily is saving for a $300 bicycle. She has saved $ 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 15

16. You will evaluate algebraic expressions and use exponents
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
Essential Question: How do you evaluate algebraic expressions and
powers?
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.