Beginning Algebra, 11th Edition

(c) 19 1/4 22 = 921 1/4^2 = 9 2/4= 9 1/2= 29 = 3

542 CHAPTER 8 Roots and Radicals

NOW TRY
EXERCISE 4
Simplify. Write each answer
in exponential form with only
positive exponents.

(a) (b)

(c) (d)
5 1/3# 5 - 2/3
5 - 4/3

a

64

125

b

2/3

11 1/3

11 2/3

7 1/4# 7 5/4

NOW TRY

Using Fractional Exponents with Variables

Simplify. Write each answer in exponential form with only positive exponents.

Assume that all variables represent positive numbers.

(a) (b)

(c) (d)

(e)

k2/3#k-1/3

k5/3

=k2/3+^1 - 1/3^2 - 5/3=k-4/3=

1

k4/3

a

z1/4

w1/3

b

5

=

1 z1/4 25

1 w1/3 25

=

z5/4

w5/3

1 x^2 y1/2 24 = 1 x^2241 y1/2 24 =x^8 y^2

p5/3

p4/3

m1/5#m3/5=m1/5+3/5=m4/5 =p5/3-4/3=p1/3

EXAMPLE 5

Use parentheses

to avoid errors. NOW TRY

OBJECTIVE 4 Use rational exponents to simplify radicals.

Simplifying Radicals by Using Rational Exponents

Simplify each radical by first writing it in exponential form.

(a)

(b)A 24 mB mÚ 0 NOW TRY

2

= 1 m1/4 22 =m2/4=m1/2= 2 m,

2693 = 1932 1/6= 9 3/6= 9 1/2= 29 = 3

EXAMPLE 6

CAUTION Errors often occur in problems like those in Examples 4 and 5

because students try to convert the expressions to radicals. Remember that the rules

of exponentsapply here.

NOW TRY
EXERCISE 6
Simplify each radical by first
writing it in exponential form.

(a) 26642 (b) A 210 yB^5

NOW TRY
EXERCISE 5
Simplify. Write each answer
in exponential form with only
positive exponents. Assume
that all variables represent
positive numbers.

(a) (b)

(c)
t-^1 #t3/4
t7/4

a

p1/5

q3/4

b

3

Ax2/3y3/2B

6

NOW TRY ANSWERS

4. (a) (b)

(c) (d) 5

5. (a) (b) (c)


6. (a) 4 (b) 2 y, yÚ 0

1

t^2

p3/5

q9/4

x^4 y^9

16

25

1

11 1/3

7 3/2

Complete solution available
on the Video Resources on DVD

8.7 EXERCISES

Concept Check Decide which one of the four choices isnotequal to the given expression.

1.

A. B. 7 C. D.

2.

A. 9 B. C. D.

3.

A.- 216 B.- 4 C. 4 D. - 2364

• 64 1/3

81

2

281 81 0.5

81 1/2

• 7 249 49 0.5

49 1/2

(d)

(e)

2 1/2# 2 -^1

2 - 3/2

=

2 1/2+^1 -^12

2 - 3/2

=

2 - 1/2

2 - 3/2

= 2 - 1/2-^1 - 3/2^2 = 2 2/2= 21 = 2

a

9

4

b

5/2

=

9 5/2

4 5/2

=

19 1/2 25

14 1/2 25

=

A 29 B

5

A^24 B

5 =

35

25 Use parenthesesto avoid errors.

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