Algebra Chapter 6 Review
Simplify the expression. Write your answer using only positive exponents.
1.
3𝑥 4 𝑦 −8
4𝑚3 (𝑛𝑝)−1 –4
)
−8(𝑚4 𝑛𝑝)7
2. (
27𝑥 −6 𝑦 4
3.
 1 
  2 
 2a 
3
Rewrite the expression as a power of a product. Answers will vary.
4.
5.
9x6 y8
64x9 y 9
Evaluate the expression.
6. 27 2 3
7.  3 125
8. 82 3  271 3
Graph the function. Describe the domain and range.
9.
y   1 4
2
x
10.
y   20.5
x
11.You deposit $675 in a savings account that earns 6% interest compounded monthly.
a. Write a function that represents the balance after t years.
b. What is the balance after 3 years?
12.You work for a design company and want to enlarge one of your designs
for a new billboard sign. You can enlarge the design by 120% every time
you run the program. The original design is 12 inches wide by 24 inches long.
a. Write a function that represents the width after t times that you run
the program.
b. How wide is the design after running the program five times?
c. How many times will you have to run the program for the design to be at least 150
feet wide?
Solve the equation. Check your solution.
13.
2  4 x 1  1
14.
32
25x  5x  3  625x  7
Determine whether the table represents an exponential growth function, an exponential
decay function, or neither. If it is exponential, write the equation in the form 𝒚 = 𝒂𝒃𝒙 .
15.
x
1
2
3
4
y
2
4
8
 16
16.
x
0
1
2
3
y
81
27
9
3
Evaluate the function for the given value of x.
17.
x
f  x  1 4 ; x   2
18.
3
19.The function Pt 
 20001.5
t
 4
x
f  x   2 1 ; x  1
2
represents the population of a small town.
a. Does the function represent exponential growth or exponential decay?
b. What is the yearly percent change in population?
c. What is the approximate monthly percent change?
d. How many people are living in the town after 3 years?
20. Simplify. Leave in simplest radical form.
a.
4 5
2 2
b. 5 2  3 7  4 
c. 3 45  7 20
d. 5 12  16 27
Answers
1.
𝑥 10
2.16𝑚100 𝑛32 𝑝32
9𝑦 10
5. Sample answer: 4a3b3 
3
3.
6.
9.

1
9
4. Sample answer: 3x3 y 4 2
8
a6
7.
5
8.
4
3
10.
domain: all real numbers;
11. a. y
range: y  0
domain: all real numbers;
range: y  0
 6751.005
12t
b. $807.76
12.a.
y  122.2 in., or y  2.2t ft
t
b. 618.4 in., or 51.536 ft
c. 7 times
13.
x  4
14.
x  31
17.
1
48
18.
1
15. Neither
19.a. exponential growth b. 50% growth
20. a.
4 10

4
10
b. 15
14  20 2
16. exponential decay
c. 4.2% growth d. 6750 people
c.  5 5
d. 58 3