Download Unit 4 Review (Exponents).

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.
b. 2.71 x 10–6
a. 8.9 x 105
8.90000
Add zeros while moving decimal point.
000002.71
(Positive exponent? RIGHT)
890,000
Rewrite in standard notation.
(Negative exponent? LEFT)
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:
2 3  2 –7  2 3(–7)  2 –4
Example 2
3–3  37  3–37  34
find a power of a power, multiply the exponents.
To
2 3
(7
) = (72)  (72)  (72)
= 72 + 2 + 2
= 76
2 3
(7 ) = 76
To divide numbers or variables with the same nonzero base, subtract the exponents.
4 –5
 4 –5– 2  4 –7
2
4
Simplify each expression. Leave in exponent form.
9. 
65  63 =
12. 8  8 =
7
59

53
18.
35  4 8

32  4 3
20.
23  68  4 5

25  66  4 5



Rewrite in exponent form.
22.

–4
15.
11. 4–5  48 =
10. (46)3 =
–3
3 2
14.   
7 
7
13. (xy) (xy) =
16.
x4

x7


19.
26  4 4

23  4 6
21.
2 2  38  4 5

2 4  38  4 3
23.
16 • 36

9 • 25


8 • 49

27 • 125


17.
9 –5

93
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