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Properties of Exponents © G. Battaly, 2013 1 March 14, 2013 Jan 2312:50 PM 4.1 Properties of Exponents College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester Community College, NY Study 4.1 # 1 95, 99, 103, 107 Homework Problems

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Page 1: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 1

March 14, 2013

Jan 23­12:50 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Study 4.1 # 1 ­ 95, 99, 103, 107

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 2: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 2

March 14, 2013

Jan 23­12:50 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

23 = 2  2  2 = 83 factors of 2

4.1  Properties of Exponents

Homework Problems

25 = 2  2  2  2  2 = 32   factors of 2

b5 = b  b  b  b  b    factors of b

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 3: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 3

March 14, 2013

Jan 23­12:50 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

2423 =(2  2  2  2)(2  2  2) = 27 =1284 factors of 2    3 factors of 2

4.1  Properties of Exponents

Homework Problems

2423 = 2(4+3) = 27 = 32

b5 b3 = b        = b 

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 4: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 4

March 14, 2013

Jan 23­12:50 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

4.1  Properties of Exponents

Homework Problems

bm bn = bm+n 

bm bn = b 

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 5: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 5

March 14, 2013

Mar 13­3:40 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

4.1  Properties of Exponents

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 6: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 6

March 14, 2013

Mar 13­3:40 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

4.1  Properties of Exponents

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 7: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 7

March 14, 2013

Mar 13­3:40 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

4.1  Properties of Exponents

odd power of negative base is negative

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 8: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 8

March 14, 2013

Mar 13­3:44 PM

4.1  Properties of Exponents

even power of negative 

    base is positive

even power of positive 

    base is positive

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 9: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 9

March 14, 2013

Jan 23­12:50 PM

4.1  Properties of Exponents

 am =  am­n an 

 am =  a an 

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 10: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 10

March 14, 2013

Jan 23­12:50 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

4.1  Properties of Exponents

Homework Problems

 am =  am­n an 

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 11: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 11

March 14, 2013

Jan 23­12:50 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

4.1  Properties of Exponents

Homework Problems

 (ab)m =  a   b 

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 12: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 12

March 14, 2013

Jan 23­12:50 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

4.1  Properties of Exponents

Homework Problems

 (ab)m =  ambm 

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 13: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 13

March 14, 2013

Jan 23­12:50 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

4.1  Properties of Exponents

Homework Problems

 (am)n =  a 

 (am)n =  amn 

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 14: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 14

March 14, 2013

Jan 23­12:50 PM

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

4.1  Properties of Exponents

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 15: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 15

March 14, 2013

Mar 13­4:09 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 16: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 16

March 14, 2013

Mar 13­4:12 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 17: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 17

March 14, 2013

Mar 13­4:15 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 18: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 18

March 14, 2013

Mar 13­4:17 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 19: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 19

March 14, 2013

Mar 13­4:19 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 20: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 20

March 14, 2013

Mar 13­4:22 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 21: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 21

March 14, 2013

Mar 13­4:28 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 22: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 22

March 14, 2013

Mar 13­4:35 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

or

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 23: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 23

March 14, 2013

Mar 13­4:38 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 24: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 24

March 14, 2013

Mar 13­4:44 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm
Page 25: Properties of Exponents · 2423 =(2 2 2 2)(2 2 2) = 27 =128 4 factors of 2 3 factors of 2 4.1 Properties of

Properties of Exponents

© G. Battaly, 2013 25

March 14, 2013

Mar 13­4:48 PM

4.1  Properties of Exponents

College Algebra Home Page

Class Notes:  Prof. G. Battaly, Westchester Community College, NY

Homework Problems

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/4_1_exponents.htm

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