Intermediate Algebra (11th edition)

Evaluating Exponential Expressions

Evaluate.

(a) 52 = 5 # 5 = 25 5 is used as a factor 2 times.

EXAMPLE 2

1.3 Exponents, Roots, and Order of Operations

3

3

(a) (b)

FIGURE 17

3 # 3 =3 squared, or 3^26 # 6 # 6 =6 cubed, or 6^3

6

6

6

NOW TRY
EXERCISE 2
Evaluate.

(a) (b)

(c) - 72

72 1 - 722

Sign of an Exponential Expression

The product of an oddnumber of negative factors is negative.

The product of an evennumber of negative factors is positive.

CAUTION As shown in Examples 2(e)and (f ),it is important to distinguish

between and

The base is a.

nfactors of a

The base is

nfactors of

Be careful when evaluating an exponential expression with a negative sign.

• a

1 - a 2 n means 1 - a 21 - a 2 # Á # 1 - a 2 - a.

• an means - 11 a#a#a# Á #a 2

- an 1 - a 2 n.

(b) is used as a factor 3 times.

(c)

(d) The base is

(e) The base is

(f )

There are no parentheses. The exponent 6 applies onlyto the number 2, not to

The base is 2.

NOW TRY

Examples 2(d) and (e)suggest the following generalizations.

• 26 = - 12 # 2 # 2 # 2 # 2 # 22 = - 64

- 2.

- 26

1 - 226 = 1 - 221 - 221 - 221 - 221 - 221 - 22 = 64 - 2.

1 - 325 = 1 - 321 - 321 - 321 - 321 - 32 =- 243 - 3.

26 = 2 # 2 # 2 # 2 # 2 # 2 = 64

2

a 3

2

3

b

3

=

2

3

#^2

3

#^2

3

=

8

27

52 means 5#5,NOT 5#2.

OBJECTIVE 2 Find square roots.As we saw in Example 2(a),

so 5 squared is 25. The opposite (inverse) of squaring a number is called taking its

square root.For example, a square root of 25 is 5. Another square root of 25 is ,

since 1 - 522 = 25.Thus, 25 has two square roots: 5 and - 5.

- 5

52 = 5 # 5 =25,

NOW TRY ANSWERS

2. (a) 49 (b) 49 (c)- 49

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