Intermediate Algebra (11th edition)

90.Use Heron’s formula from Exercise 89to find the area of a triangle with sides of lengths

91.The coefficient of self-induction L(in henrys), the energy Pstored in an electronic circuit

(in joules), and the current I(in amps) are related by this formula.

(a)Find Iif and. (b)Find Iif and

92.The Vietnam Veterans Memorial in Washington, DC, is in the

shape of an unenclosed isosceles triangle with equal sides of

length 246.75 ft. If the triangle were enclosed, the third side

would have length 438.14 ft. Use Heron’s formula from Exer-

cise 89to find the area of this enclosure to the nearest hundred

square feet. (Source: Information pamphlet obtained at the

Vietnam Veterans Memorial.)

P= 120 L= 80 P= 100 L=40.

I=

B

2 P

L

a=11 m, b=60 m, and c=61 m.

SECTION 8.2 Rational Exponents 435

246.75 ft

438.14 ft

246.75 ft

Not to scale

Apply the rules for exponents. Write each result with only positive exponents. Assume that all

variables represent nonzero real numbers. See Section 5.1.

93. 94. 95. 96.

5

5 -^1

a

2

3

b

• 3
  x^5 #x-^1 #x-^314 x^2 y^32123 x^5 y 2

PREVIEW EXERCISES

OBJECTIVES

Rational Exponents

8.2

1 Use exponential
notation for nth
roots.

2 Define and use
expressions of the
form.

3 Convert between
radicals and rational
exponents.

4 Use the rules for
exponents with
rational exponents.

am/n

OBJECTIVE 1 Use exponential notation for nth roots.Consider the product

Using the rules of exponents from Section 5.1,we can simplify

this product as follows.

Product rule:

Add exponents.

Also, by definition,

Since both and are equal to 3, it seems reasonable to define

This suggests the following generalization.

3 1/2 = 23.

A^23 B

2

13 1/2 22

A^23 B

2

= 23 # 23 = 3.

= 3 a^1 =a

= 31

= 3 1/2+1/2 am#an=am+n

13 1/2 22 = 3 1/2# 3 1/2

13 1/2 22 = 3 1/2 # 3 1/2.

If is a real number, then a1/n

n

2 2 a.

n

a

a1/n

and Examples of

Notice that the denominator of the rational exponent is the index of the radical.

4 1/2 = 24 , 8 1/3= 238 , 16 1/4= 2416 a1/n