This document contains notes from a math lesson on operations with exponents. It includes examples of multiplying and dividing terms with the same base, which involves adding or subtracting the exponents. It also covers raising an exponent to another power, which means multiplying the exponents. The document provides step-by-step workings through multiple examples and problems involving exponent rules. The objective is for students to learn how to simplify numeric and variable expressions using the laws of exponents.

1. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
Write using exponents
1. k k k k
2. m n m n
3. 5 5 5
4. 3 3 r r
Bellwork
Objective: laws of exponents
Nov 24­7:16 PM
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2. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
Multiplying Powers with the same base ­
Add the exponents
72 73
Nov 24­7:28 PM
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2

3. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
Simplify each expression.
3 33
a5 a b2
m5 m7
x2 x3 y y4
Nov 24­7:32 PM
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3

4. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
Simplify each expression.
6a3 3a
­5c2 ­3c7
Nov 24­7:34 PM
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5. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
Power to a Power ­ multiply the exponents
3
(7 )
2
Nov 24­7:36 PM
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6. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
Simplify each expression.
3
()
()
32
2
a6
Nov 24­7:39 PM
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6

7. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
Write in simplest form.
1. x2
x
3. 3c2 * 2c4
2. 6xy
9y
4. w 3t3 * t4w7
Objective: divide and simplify exponents
Oct 24­11:54 AM
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8. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
78
73
Dividing powers with the same base ‐ subtract the exponents
x4
x2
3
35
8
Oct 24­11:54 AM
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9. 4.7 & 4.8 Multiplying & Dividing Exponents
x25
x18
October 24, 2013
12m5
3m
Oct 24­11:55 AM
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10. 4.7 & 4.8 Multiplying & Dividing Exponents
3
34
4
October 24, 2013
When we have an exponent of zero the answer is
(‐8)2
(‐8)2
6b3
18b3
Oct 24­11:55 AM
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11. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
x5y6
x5y3
43
0
Oct 24­11:55 AM
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12. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
32
34
negative exponents ‐ how do we make them positive?
Oct 24­11:56 AM
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13. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
m2
m5
56
58
3y8
9y12
Oct 24­11:56 AM
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14. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
Write x2y3 without a fraction bar.
x 3y
m3n2
m6n8
Oct 24­11:56 AM
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15. 4.7 & 4.8 Multiplying & Dividing Exponents
October 24, 2013
HW worksheet
Oct 24­11:57 AM
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15