Assignment # _____ Unit 4 Review: Exponents Name ______
Standards: AF 2.1 Simplify expressions with exponents Pre-Algebra, Period ______
AF 2.2 Multiply powers with the same base
AF 2.1 Divide powers with the same base Date ______
NS 1.1 Compare rational numbers in scientific notation
Write each number in standard form.
a. 8.9 x 105 b. 2.71 x 10–6
8.90000 Add zeros while moving decimal point. 000002.71
(Positive exponent? RIGHT) (Negative exponent? LEFT)
890,000 Rewrite in standard notation. 0.00000271
1. 3.454 x 102 = ______2. 4.035 x 10–4 = ______
3. 3.847 x 107 = ______4. 7.7 x 10–3 = ______
Example 1
About 4,200,000 visit the Statue of Liberty every year. Write this number in scientific notation.
4,200,000 Move the decimal point to get a decimal greater than 1 but less than 10 (six places!).
4.2 Drop the zeros after the 2.
= 4.2 x 106 Decimal point moved SIX places to the LEFT. Use 6 as the exponent of 10.
Example 2
Write 0.000079 in scientific notation.
0.000079 Move the decimal point to get a decimal greater than 1 but less than 10 (5 places!).
7.9 Drop the zeros before 7.
= 7.9 x 10–5 The decimal point moved FIVE places to the right. Use –5 as the exponent of 10.
5. 314,000,000 = ______6. 0.0000731 = ______
7. 77,250 =______8. 8,120,000,000 = ______
To multiply numbers or variables with the same base, add the exponents.
Example 1:
Example 2
To find a power of a power, multiply the exponents.
(72)3 = (72) · (72) · (72)
= 72 + 2 + 2
= 76
(72)3 = 76
To divide numbers or variables with the same nonzero base, subtract the exponents.
Simplify each expression. Leave in exponent form.
9. 65 · 63 = 10. (46)3 = 11. 4–5 · 48 =
12. 87 · 8–4 = 13. (xy)–3(xy)7 = 14.
15. 16. 17.
18. 19.
20. 21.
Rewrite in exponent form.
22. 23.
Bingo Answers:
Evaluate the power
1. 16
2. 27
3. 125
4. 1
5. 0
6. 64
Fraction Powers
7. 8/27
8. 16/25
9. 16/81
Standard Notation
10. 540.1
11. 0.05401
12. 54,010
Scientific Notation
13. 5.401 x 103
14. 5.401 x 104
15. 5.401 x 107
Multiplying Powers
16. 47
17. 74
18. (xy)–3
19. (xy)5
Powers of Powers
20. (xy)18
21. 424
Rewrite with Exponents
22. 32 • 42/62 • 52
23. 33 • 23/42 • 52
Dividing Powers
24. 34
25. 59
26. 150 = 1
Dividing Powers (Multi)
27. 33 • 54
28. 22/32 = 4/9
29. 6/52 = 6/25
30. 32/72 = 9/49