Unit Summary 2
Class: Math 8
Unit 2: Exponents and Scientific Notation – chapter 1 & 2
I. Big Ideas:
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Students will understand that you can use exponential notation to represent repeated multiplication
of the same factor.
Students will understand that monomial expressions and formulas can be simplified and evaluated.
Students will understand exponents and radicals are inverses of each other.
Students will understand that relationships can be described for mathematical situations that have
numbers repeat in predictable ways.
Students will understand that scientific notation is a way of writing numbers that makes it easier to
work with very big or very small numbers.
II. Topics that will be covered:
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6.
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III.
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Prime Factorization
Multiplication properties of exponents
Division properties of exponents
Negative and zero exponents
Scientific notation (adding, subtracting, multiplying, dividing)
Simplifying radicals
Real world problems with exponents and scientific notation
Essential Questions:
What is simplest form?
How is the power rule related to the product rule?
What does a negative exponent mean?
What does it really mean to “cancel” when simplifying fractions?
Where can I use scientific notation and radicals in the real-world?
What happens with the exponents when the same bases are multiplied or divided?
IV.
Sample questions to answer by the end of the unit:
Write all answers in simplest form.
1. 2x2(3x2 – 5x – 12)
2. 12x(3x – 5) – 6x(2x – 4)
3. 12x6 – 24x4 – 8x2
4x
4. (2x3y7)4
5. (10xy)3
6. 12x2y9
18x7y4
7. (4x7y9)(-2x3y4)
8. 27x5y6
3x8y4
Write each in scientific notation.
9. 25,000
10. 0.0089
11. 0.00000406
12. 805,000,000
Determine whether each number is written in scientific notation. If it is not, write it in scientific
notation.
13. 950 x 105
14. 72.35 x 109
15. 1.6 x 107
16. 0.26 x 10-13
Write each expression so that all exponents are positive.
17. b-4g3d-5
18. x-4y8g-2
x3y16g7
19. (x3)(x-5)(x-4)
20. (3x2y-5)-2
Solve for g.
21. g2 = 36
22. 2g = 1
23. 2g = ½
24. 2g = 0.25
Add, subtract, or multiply as indicated. Leave answers in scientific notation.
25. 5.1 x 105 + 4.5 x 105 =
26. 8.1 x 108 – 6.7 x 108 =
27. 2.3 x 103  3.6 x 107 =
28. 6.77 x 1010 + 5.4 x 109 =
29. 6.5 x 106 – 4.9 x 105 =
30. 3.1 x 104 • 2.2 x 105 =
31. The Georgia Aquarium in Atlanta is about 2.63 x 103 inches long, 1.26 x 102 inches wide, 3 x 101
inches deep at its largest point. Find its approximate volume.
32. Fruits (per 100 grams)
Apple
Orange
Pear
Energy (Cal)
4.9 x 104
6.2 x 104
3.5 x 104
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Calculate the total energy of the three fruits. Write your answer in scientific notation.
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Find the difference in energy contained between 100 grams of apple and 100 grams of pear.
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How many times more energy does 100 grams of orange have compared to 100 grams of apple?
Round to the nearest tenth.