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Name__________________________________
Hour_________
Chapter 5 Final Exam Review
5.1-5.3/5.5-5.7/5.9/5.11
RULE 1
MULTIPLYING EXPONENTS
RULE 2
POWER TO A POWER
x3 • x4 = x3+ 4 = x 7
(S3)4 = S_3 * 4__ = S_12_
Q4 • Q6 = Q_4 + 6__ = Q10
(Z2)5 = Z_2*5__ = Z _10_
(x+p)7 • (x+p)4 = (x+p)7 + 4__ = (x+p)11
***YOU ________ THE EXPONENTS.
THE BASE STAYS THE _________
RULE 3
DIVIDING EXPONENTS
x5
= x _5-7___ = x _-2_
x7
p9
p4
= p_9-4__ = p_5
*****YOU _____________
THE EXPONENTS. The base stays
the _________
h0 =____
RULE 4
ZERO POWER
7000 = ________
(x + 8)0=
****you __________ the exponents
*****anything raised to the ___
The base stays the _______________
power will equal _____!
To evaluate means to get an answer
use your calculator!!
74 = 7 find the ^ key and then 4 =
Or 7 7
7 7 = 2,401
Evaluate to a single number.
To write in exponential form you
count the number of time you SEE
the base. The base does not change
and the amount of times you count it
is the exponent. x x x x x = x5
1. 43
2. 50
3. 102
4. If you were asked to evaluate 64 power your answer would be
a. 1,296
b. 24
c. 216
5. Evaluate means to do what in mathematics?
a. simplify
b. get an answer
c. DON’T TOUCH
b. 0
c. 1
6. The correct answer to 1000 is
a. 100
Write in exponential form.
7. n
n
n
4 × 4
10.
g×g × g
9. (3)(3)(3)(3)
8.
11. What would the correct exponential form for 6
a. 67
12. If you were to write x
a. x 3
6
6
b. 76
x
x
6
6
6
6 look like?
c. 279,936
x in exponential form, the right way would be;
b. x4
c. 4x
13. What is the Product Law of Exponents? (Rule Number 1)
a. ADD exponents base stays the same
b. SUBTRACT exponents, base stays the same
c. MULTIPLY exponents, base stays the same
2
NOW Use the Product Law (Rule number 1) (5.1)
14. 56 × 58
15. 42 × 46
16. x10 × x8
17. (X + P)
11
× (X+ P)6
18. x 3 • x5 can be simplified to
a. x15
b. x-2
c. x8
19. If you were to simplify (m + n)3 • (m + n)3 , what would be the correct BASE for you
answer?
a. (m + n)
b. 6
c. there is no base
20. you were to simplify (m + n)3 • (m + n)3 , what would be the correct power for you answer?
a. (m + n)
b. 6
c. 9
21. What is the Power of a Power Law of Exponents? Rule number 2)
a. ADD exponents base stays the same
b. SUBTRACT exponents, base stays the same
c. MULTIPLY exponents, base stays the same
Use the Power Law (Rule number 2)(5.1)
22. (x6)2
__________________
24. (22)4 __________________
3
23. (72)3
_________________
25. (x2)2
__________________
26. When evaluating [(x– m)2]3 , what would be the correct answer?
a. (x – m ) 5
b. (x – m )-1
c. (x – m )6
27. When evaluating [(2w – 3x)2]5 , what would be the base to the correct answer?
a. 2w – 3x
b. 10
c. 7
28. When evaluating [(2w – 3x)2]5 , what would be the exponent to the correct answer?
a. 2w – 3x
b. 10
c. 7
29. What is the Quotient Law of Exponents? (Rule number 3)
a. ADD exponents base stays the same
b. SUBTRACT exponents, base stays the same
c. MULTIPLY exponents, base stays the same
Now Use the Quotient Law (Rule number 3)
30.
31. (n + m)9 ÷ (n + m)5
(v) 2 ÷ (v) 1
32. m9 ÷ (m)2
33. (h)10 ÷ (h)11
34. x7 can be simplified to ?
x4
a. x3
b. x11
c. x28
b. (x + p)-3
c. (x + p)3
35. (x + p)7 will simplify to?
(x +p)10
a. x -3
4
If they ask you to change a NEGATIVE exponent to a Positive exponent, you just use the
RECIPROCAL of the given number. 1 will always be on top and the base goes to the
BOTTOM of the fraction. The EXPONENT stays with the base, and becomes POSITIVE.
EXAMPLE: 5 -5 =
x-7 = 1
x7
1
55
Directions Rewrite using a positive exponent. (5.2)
36.
38.
5–3 ________________
–3
37.
x–5 ________________
39.
8–5 ________________
10 ________________
y–7 would look like ________ with a positive exponent.
40.
a. y 7
b. 1
7
c. 1
y7
41. The reciprocal of and whole number will have a ____ on the top of the fraction.
a. itself
Write 500.37
b. 1
c. -2
and
0.0041 in scientific notation.
Step 1
500.37
Step 2
Count decimal places: 2 to the left.
Step 3
5.0037 • 102
(Rule: Use a positive exponent if the
decimal point moved left.)
5
Put the following numbers into Scientific notation. (5.3)
42. 55,000
43. 62,100,000
44. .000000589
45. When putting numbers into scientific notation, if you have to move the decimal to the LEFT, your exponent
will be
a. positive
b. negative
46. What will the following number look like in scientific notation: 561,000,000
a. 5.61 8
b. 5.61 x 108
c. 5.61 x 10-8
47. What will 0.000012 look like in scientific notation.
a. 1.2 x 10-5
b. .12 x 10-4
c. 12 x 10-6
48. When putting numbers into scientific notation, we must move the decimal so that the number is
between___________
a. 1 and 15
b. 1 and 5
c. 1 and 10 (less than 10)
49. The exponent that is attached to the base 10 tells you how many times you moved the ________
a. decimal
b. number
c. base
Rewrite into Standard Form (5.3)
50. 8.34 x 1010
51. 9.94 x 107
52. 6.12 x 103
53. When writing numbers in standard form, if the exponent is positive you move the decimal to
the ________________
a. left
b. right
54. When writing numbers in standard form, if the exponent is negative you move the decimal
to the ___________________
a. left
b. right
6
Fill in the blanks with the correct name of the polynomial and the correct
degree of the polynomial. (5.5)
Expression
Name of the Polynomial
Degree
3n2 + 2n
55. ___________________
k3 – 2k2 + k – 4
Polynomial
56. ________________
5x + 6
Binomial
57._________________
3x2
58 ________________
2
7y2 + 4y – 5
59. ________________
60. ________________
n4 + n2 – 8n – 8
61. ________________
62. __________________
2
63. The degree on any polynomial tells you what information?
a. the highest exponent
b. how many terms
c. the biggest coefficient
64. 5x10 is an example of what type of polynomial?
a. binomial
b. monomial
c. trinomial
65. 5x10 + 2x8 – 7x is a trinomial raised to ______ degree
a. 7
b. 8
c. 10
b. 2
c. 3
66. A binomial has how many terms in it?
a. 1
67. 5x2 and 17x are like terms.
a. true
b. false
7
ADD the polynomials (5.6) Remember to rewrite it like a regular addition
problem.
68. (5k3 – 9k2 + 12k – 3) + (k3 + 10k2 + k + 14)
69. (3y4 + 2y2
-
7y) + (5y3 - 2y2 + 2y + 9)
70. You must make sure that the variable and the ____________ match in order for the terms to be like terms
a. coefficient
b. variable
c. exponent
71. When adding 2x + 6x , the answer will be
b. 8x2
a. 8x
c. cannot be combined
SUBTRACT
72. (4n2 - 8n + 3) – (3n2 + 5n
- 4)
73. (6x4 – x3 + 12x + -16) – (5x3 + 2)
74. When subtracting (4n2 – 8) – (2n2 + 2) you get the answer of
a. 6n2 – 6
b. 2n2 – 10
75. 8x10 and 17 x10 are like terms.
a. true
b. false
8
c. 2n2 – 6
Multiply the following polynomials.
Remember to multiply big numbers and add little
numbers!
77. (c3)(c2 – 3c + 9)
76. (k + 4)(3k+- 6)
78. (3b + 3)(2b+ 9) would result in which answer?
a. 6b2 + 33b + 27
c. 6b2 + 24b
a. 30b +27
79. (y)(y2 – 2y) would give you what answer?
a. y3 – 2y2
b. y2 – 2y
c. 3y - 2y2
Divide each of the polynomials. Write your final answer on the line.
80. (15n2 – 5n + 45) ÷ 5
81. (16y3 – 4y) ÷ (4y)
82. (2k7 – 4k6 + 16k5 – 22k3 – 6k2) ÷ (2k2) would give you what answer?
a. k7 – 4k6 + 16k
b. k5 – 2k4 + 8k3 – 11k – 3
9
c. 2k5 – 4k4 + 16k3 – 22k – 6
83. When you look like you are trying to divide like variables with exponents, you really __________ the
exponents.
a. add
b. multiply
2
Directions Evaluate P(x, y) = x
c. subtract
+ xy + y2 for each set of values.
84. x = 1, y = –2
85. x = –1, y = 6
86. What would you get if x = 4, y = –3 in the following polynomial, x2 + xy + y2 .
a. 13
b. 5
c. 37
b. -8
c. 16
87. (-4)2 will give you the answer of
a. -16
10