Beginning Algebra, 11th Edition

350 CHAPTER 5 Exponents and Polynomials

5.1 The Product Rule and Power Rules

for Exponents

For any integers mandn, the following are true.

Product Rule

Power Rules (a)

(b)

(c) a

a

b

b

m

=

am

bm

1 bZ 02

1 ab 2 m=ambm

1 am 2 n=amn

am#an=am+n

Perform the operations by using rules for exponents.

a

2

3

b

4

=

24

34

16 a 25 = 65 a^5

13422 = 34 #^2 = 38

24 # 25 = 24 +^5 = 29

QUICK REVIEW

CONCEPTS EXAMPLES

5.2 Integer Exponents and the

Quotient Rule

If then for integers mandn, the following are true.

Zero Exponent

Negative Exponent

Quotient Rule

Negative-to-Positive
Rules

a

a

b

b

• m
  =a

b

a

b

m

1 bZ 02

a-m

b-n

=

bn

am

1 bZ 02

am

an

=am-n

a-n=

1

an

a^0 = 1

aZ0, Simplify by using the rules for exponents.

a

6

5

b

• 3
  =a

5

6

b

3

4 -^2

3 -^5

=

35

42

48

43

= 48 -^3 = 45

5 -^2 =

1

52

=

1

25

150 = 1

5.3 An Application of Exponents:

Scientific Notation

To write a number in scientific notation

where

move the decimal point to follow the first nonzero digit.

1.If moving the decimal point makes the number less,
nis positive.
2.If it makes the number greater, nis negative.
3.If the decimal point is not moved, nis 0.

a: 10 n, 1 ...|a| 6 10,

Write in scientific notation.

Write without exponents.

8.44* 10 -^6 =0.00000844

3.25* 105 =325,000

4.8=4.8* 100

0.0051=5.1* 10 -^3

247 =2.47* 102

5.4 Adding and Subtracting Polynomials;

Graphing Simple Polynomials

Adding Polynomials
Add like terms.

Subtracting Polynomials
Change the signs of the terms in the second polynomial
and add the second polynomial to the first.

Add.

7 x^2 + 3 x+ 4

5 x^2 - 2 x+ 7

2 x^2 + 5 x- 3

Subtract.

=- 3 x^2 + 7 x- 10

= 12 x^2 + 5 x- 32 + 1 - 5 x^2 + 2 x- 72

12 x^2 + 5 x- 32 - 15 x^2 - 2 x+ 72

(continued)

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