Station 1 – Operations with Positive Exponents
Station 1 key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
𝑎6
8𝑎3 𝑏3
−18𝑥 7
𝑏15
−27𝑥 9
4𝑥 4 𝑦 6
125𝑥 6 𝑦 12
216𝑥 12 𝑦 18
64𝑥 9 𝑦 9
49𝑥 2 𝑦 2
𝑥2
−6𝑐
−3𝑎2 𝑏3
6𝑐𝑑 3
11𝑦 5 𝑧 15
Station 2 – Operations with positive and negative exponents
Station 2 key
1.
2.
1
𝑥 20
2
𝑥8
3. 2𝑛8
4. 8𝑣 4
5. 8𝑥 8 𝑦 6
6.
2𝑦 2
𝑥
Station 3 – Operations with positive, negative, and zero exponents
Station 3 key
13. 1
14. 𝑥 4 𝑦 3
15.
16.
1
8𝑎8 𝑏 2
𝑥3
4𝑦 5
17. 2𝑘 8
18.
1
2𝑥 5
Station 4 – Working with rational exponents
1. 𝟏𝟔
2.
𝟑
𝟒
𝟏
𝟏𝟐𝟓𝟑
𝟒
3. 𝟑𝟐𝟓
4. 𝟖
𝟐
𝟑
5. 𝟔𝟒
𝟐
𝟑
𝟏
6. 𝟐𝟓𝟒
𝟖𝟏
−𝟑
𝟐
7. (𝟏𝟎𝟎)
Station 4 key
1. 8
2. 5
3. 16
4. 4
5. 16
6. 5
7.
1
2
103 1000
93
=
729
Station 5 – Working with variables and rational exponents
4
3
3
5
1
3
1
5
1. (7𝑞 ∙ 6𝑟 ) ∙ (7𝑞 ∙ 6𝑟 )
5
2
3
4
3
2
5
4
2. (3ℎ ∙ 2𝑘 ) ∙ (2𝑘 ∙ 3ℎ )
1
6
1
2
1
4
5
6
3. (8𝑝 ∙ 5𝑚 ) ∙ (8𝑝 ∙ 5𝑚 )
Challenge problem:
Station 5 key
𝟓
𝟑
𝟒
𝟓
𝟓 𝟒
𝟑 𝟓
1. 𝟒𝟗𝒒 ∙ 𝟑𝟔𝒓 = 𝟏𝟕𝟔𝟒𝒒 𝒓
𝟏𝟓
𝟒
𝟗
𝟒
𝟏𝟓
𝟒
2. 𝟗𝒉 ∙ 𝟒𝒌 = 𝟑𝟔𝒉 𝒌
𝟖
𝟔
𝟓
𝟏𝟐
3. 𝟐𝟓𝒎 ∙ 𝟔𝟒𝒑
𝟗
𝟒
𝟒
𝟑
𝟓
𝟏𝟐
= 𝟏𝟔𝟎𝟎𝒎 𝒑
Challenge problem:
*simplify inside the parentheses first and it will be easier*
𝟒𝒙𝟔 𝒚𝟖
𝒛𝟒
Station 6 – Using Scientific Notation
#1-3 Simplify and write your answer in scientific notation.
1.
3 × 105
2 × 10−6
2. (3 × 108 )3 (2 × 108 )
3.
(32 × 105 )
(2 × 10−6 )4
4. Suppose a white dwarf star has a diameter of approximately
star? Express it in scientific notation. Round to the hundredths.
km. What is the radius of the dwarf
Station 6 key
1. 1.5 × 1011
2. 5.4 × 1033
3. 2 × 1029
4. 9.04 × 103
Station 7 – Using Scientific Notation
1. A textile factory produces 1.08 × 108 yards of fabric every year. If a factory is in operation 360 days a year, what is the
average number of yards of fabric produced each day? Give your answer in scientific notation.
2. The estimated number of insects on Earth is 1 × 1019 . The number of people on Earth is estimated to be 6 × 109 .
What is the estimate for the number of insects per person?
A. 1.7 × 108
B. 1.7 × 109
C. 1.7 × 1010
D. 1.7 × 1011
3. Suppose a white dwarf star has a diameter of approximately 1.8083 × 104 𝑘𝑚. Use the formula 4𝜋𝑟 2 to find the
approximate surface area of the star. Use 3.14 for 𝜋.
A. 1.64 × 1010 𝑘𝑚2
B. 2.27 × 105 𝑘𝑚2
C. 1.03 × 107 𝑘𝑚2
D. 1.03 × 109 𝑘𝑚2
4. And a little extra:
You have learned how to make lightweight plant containers using a mixture of peat, sand, and cement. You are going to
4
take these skills and make lawn ornaments in the shapes of spheres. Use the formula 𝑉 = 𝜋𝑟 3 to write an expression
for the volume of spheres that have a radius of
fractions, not decimals).
1
2
𝑓𝑡,
3
2
𝑓𝑡, and
3
4
3
𝑓𝑡. Leave answers in terms of 𝜋 (answers should be
Station 7 key
1. 3 × 105
2. B
3. D
4
1
1
4. 𝑉 = 3 𝜋 ∙ 8 = 6 𝜋
4
𝑉 = 3𝜋 ∙
27
8
9
= 2𝜋
4
27
9
𝑉 = 3 𝜋 ∙ 64 = 16 𝜋
Station 8 – Can you spot the errors?
Jim Nasium turned in the following quiz paper. Determine which are correct and which are not.
Name: Jim Nasium
1. (53 )−1 = −125
1
4
2. (16) = 4
4
3
3. (−8) =
1
2
−
4. (81)
Exponent Quiz
6.
7.
−32
3
= −9
5. (49)−2 =
2
3
(64) = 16
1
4
(81) ∙ (2)−1 = 2
1
2
1
2
8.
(9) ∙ (4) =
9.
1
2
2
(100) ∙ (25)−2 =
1
7
3
1
2
2
10. (100 ) = 10
1
25
Station 8 key
1.
1
Incorrect because 5−3 = 125
1
2.
3.
Incorrect because
(24 )4
=2
4
3
Incorrect because (−8) =
1
2 −2
4
(−23 )3
= 9−1 =
4.
Incorrect because (9 )
5.
Incorrect because (49)−2 =
6.
CORRECT!!
7.
1
4 )4
Incorrect because (3
1
8.
9.
10.
Incorrect because
(32 )2
1
9
(49)2
1
3
2
2
∙ (2)−1 = 3 ∙ =
1
2 )2
∙ (2
1
2 )2
Incorrect because (10
1
= (−2)4 = 16
1
2
∙
1
(25)2
=3∙2=6
=
10
625
=
2
125
2
Incorrect because (100 ) = 1001 = 100
POOR JIM NASIUM ONLY DID ONE PROBLEM CORRECTLY! 