This document contains examples and practice problems for evaluating algebraic expressions and powers. It includes steps like substituting values for variables, multiplying terms when evaluating powers, and identifying expressions in word problems. Practice problems cover topics like evaluating expressions for various values of variables, writing expressions in word form, finding volumes using side lengths and cube powers, and setting up and solving word problems algebraically.

1. Warm-Up Exercises
Perform the indicated operation.
1. 12 1.5
2. 3.3 7
ANSWER 8
ANSWER 23.1

2. Warm-Up Exercises
3. 11.6 – 5.9
ANSWER 5.7
4. Julia ran 10 miles last week and 8 miles this week.
How many more miles did she run last week?
2
3
5
6
ANSWER 1 mi5
6
Perform the indicated operation.

3. Warm-Up Exercises
Substitute 3 for n.
Multiply.= 39
Subtract.= 2
Substitute 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
9
3
b. 9
n
=
c. n – 1 =
Substitute 3 for n.
Add.= 11
d. n + 8 =
3 – 1
3 + 8

4. Warm-Up ExercisesGUIDED PRACTICE for Example 1
= 12
= 6
= 4
Evaluate the expression when y = 2.
1. 6y
2. 8
y
3. y + 4
= 94. 11 – y

5. 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.

6. 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

7. 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
1
2
1
2
1
2
z to the fifth powerd. z5 z z z z z

8. 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

9. 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

10. Warm-Up ExercisesEXAMPLE 4 Evaluate powers
Evaluate the expression.
a. x4
= 24
= 16
= (1.5)(1.5)(1.5)
= 3.375
= 2 2 2 2
b. n3
= 1.53
b. n3
when n = 1.5
SOLUTION
a. x4
when x = 2

11. 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

12. Warm-Up ExercisesGUIDED PRACTICE for Example 4
Evaluate the expression.
11. d4
when d =
1
3
11. 1
81
ANSWER

13. 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.

14. 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

15. 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

16. Warm-Up ExercisesDaily Homework Quiz
1
3
3
4.
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.
$171.75ANSWER
ANSWER 1
27