Intermediate Algebra (11th edition)

Using Negative Exponents

In parts (a) – (f ), write with only positive exponents.

(a) (b)

(c) (d)

Base is 5z. Base is z.

(e) (f )

( What is the base here?) ( What is the base here?)

In parts (g) and (h), evaluate.

(g)

a c+

b c=

a+b

= c

7

12

1 3 #

4 4 =

4 12 ;

1 4 #

3 3 =

3

= 12

4

12

+

3

12

=

1

3

+

1

4

3 -^1 + 4 -^1

1 - m 2 -^2 = mZ 0

1

1 - m 22

- m-^2 = - mZ 0 ,

1

m^2

,

5 z-^3 = 5 a zZ 0

1

z^3

b =

5

z^3

15 z 2 -^3 = zZ 0 ,

1

15 z 23

,

6 -^1 = a-n=a^1 n

1

61

=

1

6

2 -^3 = a-n=a^1 n

1

23

EXAMPLE 3

266 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions

CAUTION A negative exponent does not indicate that an expression repre-

sents a negative number.Negative exponents lead to reciprocals.

Not negative - 3 -^2 =- Negative

1

32

= -

1

9

3 -^2 =

1

32

=

1

9

NOW TRY
EXERCISE 3
Write with only positive
exponents.

(a)

(b)

(c)

(d)Evaluate. 4 -^1 + 6 -^1

4 k-^3 , kZ 0

13 y 2 -^6 , yZ 0

9 -^4

NOW TRY
EXERCISE 4
Evaluate.

(a) (b)

10 -^2

2 -^5

1

5 -^3

(h)

a c-

b c=

a-b

=- c

3

10

=

2

10

-

5

10

=

1

5

-

1

2

5 -^1 - 2 -^1

NOW TRY

Definition of negative exponent

CAUTION In Example 3(g),note that The expres-

sion simplifies to as shown in the example, while the expression

13 + 42 -^1 simplifies to 7 -^1 ,or 71 .Similar reasoning can be applied to part (h).

7

3 12 ,

(^1) + 4 - 1

3 -^1 + 4 -^1 Z 13 + 42 -^1.

Using Negative Exponents

Evaluate.

(a)

Multiply by the reciprocal of the divisor.

(b) = NOW TRY

1

23

,

1

32

=

1

23

#^3

2

1

=

32

23

=

9

8

1

23

1

32

2 -^3

3 -^2

=

= 1 ,

1

23

= 1 #

23

1

= 23 = 8

1

23

1

2 -^3

=

EXAMPLE 4

NOW TRY ANSWERS

(a) (b)

(c) (d)

(a) 125 (b)
8
25

5 12

4
k^3

1 13 y 26

1 94

Definition of negative exponent

Get a common denominator.