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Unit 5 Review

Total questions: 61

Worksheet time: 3hrs 54mins

Name
Class
Date
1.
a)
2a2b6
b)
1/2a2b6
c)
b6/2a2
d)
2b6/a2
2.
Evaluate the expression using the Same Base, Division rule.
a)
214 z13
b)
22/z7
c)
214/ z7
d)
22 z7
3.
a)
2a2b6
b)
1/2a2b6
c)
b6/2a2
d)
2b6/a2
4.

Write the above expression in exponential form.

a)
b)
c)
d)
5.

Write the above expression in exponential form.

a)
b)
c)
d)
6.

Write the above expression in exponential form.

a)
b)
7.

Rewrite x2/3 as a radical.

a)

√x3

b)

∛x2

c)

2x3

d)

3x2

8.
Rewrite in radical form.
a)
A
b)
B
c)
C
d)
D
9.
Rewrite in radical form.
a)
A
b)
B
c)
C
d)
D
10.
A rectangle has an area of 24m² and a base of 4m. What is the height?
a)
20m
b)
6
c)
6m
d)
6m²
11.
A rectangle has an area of 34x²y⁸ and a base of 17xy.  What is the height?
a)
2xy⁷
b)
17xy
c)
17xy³
d)
2xy
12.
What is the side length of a square that has an area of 40 in2?
a)
20 in
b)
10 in
c)
1600 in
d)
6.3 in
13.

The expression (x8)(x-5) is equivalent to the expression xn. What is the value of n?

a)

-40

b)

-13

c)

13

d)

3

14.

The expression (34)(3-7) is equivalent to the expression xn. What is the value of n?

a)

-28

b)

3

c)

-3

d)

-11

15.

The expression (d-8)(d10) is equivalent to the expression xn. What is the value of n?

a)

2

b)

-80

c)

-810

d)

18

16.
Simplify:  √28
a)
7√2
b)
2√7
c)
4√7
d)
2√14
17.
Simplify:
a)
8x9
b)
8x3
c)
8x4√x
d)
8x3√x
18.
Simplify:
a)
5x√2
b)
100x√2
c)
10x√2
d)
10√2x
19.

Which radical is simplified?

a)
b)
c)
d)
20.
Select the correct graph for each inequality.
a)
A
b)
B
c)
C
d)
D
21.
Select the correct graph for each inequality.
a)
A
b)
B
c)
C
d)
D
22.
Select the correct graph for each inequality.
a)
A
b)
B
c)
C
d)
D
23.

Which equation matches the table?

a)

f(x) = 3x + 9

b)

f(x) = x + 9

c)

f(x) = x + 3

d)

f(x) = 12x - 3

24.

Which equation matches the table?

a)

f(x) = x + 5

b)

f(x) = 6x

c)

f(x) = x + 6

d)

times 6

25.
Which equation matches the table?
a)
y = 3x + 9
b)
y = x + 9 
c)
y = x + 3
d)
y = 12x - 3
26.

What is the algebraic equation for this table?

a)

f(x) = x + 3

b)

f(x) = 3x

c)

f(x) = x ÷ 3

d)

f(x) = x - 3

27.
What is the equation of the linear function?
a)
y = -3x + 10
b)
y = -3x + 16
c)
y = 3x + 10
d)
y = 3x + 16
28.

Simplify the following expression:


2x3y5 ⋅ 5xy2

a)

10x4y7

b)

7x4y7

c)

10x3y10

d)

7x3y10

29.

Simplify the following expression:


(2a2b4z)(6a3b2z5)

a)

8a5b6z6

b)

12a6b8z5

c)

12a5b6z6

d)

8a6b8z5

30.

Simplify the following expression:


5a3b5 ⋅ 3a2b2

a)

8a5b3

b)

15a5b7

c)

8a5b7

d)

15a5b3

31.
Evaluate the expression using the quotient rule.
a)
x13
b)
x5
c)
x36
d)
x-5
32.
Evaluate the expression using the quotient rule.
a)
c7
b)
1/c7
c)
1/c17
d)
c60
33.
Evaluate the expression using the quotient of powers rule.
a)
a8b13
b)
a2b7
c)
a15b30
d)
a8b7
34.
Simplify the following expression: 
xy-7
a)
xy7
b)
x/y7
c)
x7/y
d)
x7y
35.
Rewrite using a positive exponent.
2w-13
a)
-w13
b)
2/w13
c)
2/w-13
d)
2w13
36.

Simplify 3a-1c-5/ d0

a)

1

b)

3/ac5

c)

3a/c5

d)

1/3a1c5d

37.

Find the volume of a cube whose side measures 2ab

a)

23a3b3

b)

2ab3

c)

6a3b3

d)

6ab

38.

Find the volume of a cube whose side measures 2x.

a)

2x3

b)

8x

c)

8x3

d)

8x4

39.

Find the volume of a cube whose side measures 2x2y4.

a)

2x6y12

b)

2x5y7

c)

8x6y12

d)

8x5y7

40.

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out (all) the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels? (Hint: How much are the coins worth?)

a)

d + n = 6.60

.10d + .05n = 80

b)

d + n = 80

d + n = 6.60

c)

d + n = 80

.10d + .05n = 6.60

41.

Simplify completely.

a)

3v√2v

b)

3v√2v3

c)

v√18v

d)

9v√v

42.
Simplify:
a)
8x9
b)
8x3
c)
8x4√x
d)
8x3√x
43.
Simplify. 
a)
5x8y10√10x
b)
5x4y5√10x
c)
5x4y5√2x
d)
5√2x9y10
44.
a)

x4y4

b)

x8y4

c)

x-4y12

d)

x8y12

45.
a)
a
b)
b
c)
c
d)
d
46.

The length of a rectangle is 4a4b5 and the width is 3a2b3, what is the expression that represents the area of the rectangle?

Area = length ⋅ width

a)
12a6b8
b)
7a6b8
c)
12a8b15
d)
12a2b2
47.
If a rectangle has a height of 5x2y7 and a width of 3x3y, what is the area? (Hint: Multiply width by height to get area of a rectangle)
a)
8x5y8
b)
15x6y7
c)
8x6y7
d)
15x5y8
48.

1.) What expression describes the area of a rectangle that has a width of (-2a2b-4z) and a length of (6a3b2z5)?

a)

8a5b6z6

b)

12a6b-8z5

c)

-12a5z6 /b2

d)

12a5b2z6

49.

Which expression describes the area in square units of a rectangle that has a width of 7a2 and a length (5a6b)2?

a)

35a14b2

b)

175a12b2

c)

175a14b2

d)

35a14b

50.

A piggy bank contains 100 coins consisting of nickels and dimes. The total value of the coins is $8.50. Which set of equations can be used to determine the number of nickels, n, and the number of dimes, d, in the piggy bank.

a)

.5n + .10d = 8.50

n + d = 100

b)

.05n + .10d = 8.50

.05n + .10d = 100

c)

.05n + .10d = 100

n + d = 8.50

d)

.05n + .10d = 8.50

n + d = 100

51.

Sam has a total of 30 nickels and dimes worth $2.40. Which set of equations can be used to determine the number of nickels, n, and the number of dimes, d?

a)

n + d = 2.40

n + d = 30

b)

.05n + .10d = 2.40

n + d = 30

c)

n + d = 2.40

.05n - .10d = 30

d)

.10n + .05d = 2.40

n + d = 30

52.

A circle has a radius of -2mn4. What is the area of a circle?

a)

4πm2n8

b)

-2πmn8

c)

-22πm2n8

d)

-4πm2n8

53.

A circle has a radius of 3m2n3. What is the area of a circle?

a)

6πm4n5

b)

9πm4n5

c)

3πm4n6

d)

9πm4n6

54.

A circle has a radius of 4a3. What is the area of a circle?

a)

8πa5

b)

16πa5

c)

8πa6

d)

16πa6

55.

Write expression is equivalent to  3a−4b224a2b−1\frac{3a^{-4}b^2}{24a^2b^{-1}}  

a)

 −21b3a6\frac{-21b^3}{a^6}  

b)

 a−6b38\frac{a^{-6}b^3}{8}  

c)

 b38a6\frac{b^3}{8a^6}  

d)

 b8a2\frac{b}{8a^2}  

56.

 3x2y412x4y6\frac{3x^2y^4}{12x^4y^6}  

a)

 x2y24\frac{x^2y^2}{4}  

b)

 −9x2y2-9x^2y^2  

c)

 4x6y104x^6y^{10}  

d)

 4x2y24x^2y^2  

57.

 2uv4(4v−1)(2u8)\frac{2uv^4}{\left(4v^{-1}\right)\left(2u^8\right)}  

a)

 v54u7\frac{v^5}{4u^7}  

b)

 4u4v12\frac{4}{u^4v^{12}}  

c)

 v126u3\frac{v^{12}}{6u^3}  

d)

 v4u9\frac{v}{4u^9}  

58.

 8xy6x5yz−2\frac{8xy}{6x^5yz^{-2}}  

a)

 4z23x4\frac{4z^2}{3x^4}  

b)

 86x4z2\frac{8}{6x^4z^2}  

c)

 4y2z2x4\frac{4y^2z^2}{x^4}  

d)

 2z2x4\frac{2z^2}{x^4}  

59.

 (a2)3(8a3)(2a3)3\frac{\left(a^2\right)^3\left(8a^3\right)}{\left(2a^3\right)^3}  

a)

 a2a^2  

b)

 8a68a^6  

c)

 8a28a^2  

d)

 11  

60.

Whic expression represents the area of a rectangle with sides measuring 5a2bc3 and 9ab4c2 units?

a)

45a2bc10

b)

-9abc13

c)

14a3b5c5

d)

45a3b5c5

61.

Whic expression represents the area of a rectangle with sides measuring 6x2y4 and -8x3y6 units?

a)

48x5y10

b)

48xy

c)

-48x-1y-2

d)

-48x5y10

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