Algebra Demystified 2nd Ed

Chapter 5 e X P O N e N T S a N D r O O T S 123

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5

9.

1

8

1

2

2

2

2

2

2

4 2 4 312

4 32

4 32

4 32

4 444

3

xy xy

xy

xy

xy

xy

=⋅==^4 xy^22

4 4

4 32

2

2

()xy^2

xy

xy

=

10.^4
27

4

3

3

3

49

(^33)
5
5
5 331
5 224
5 224
5 24
xy xy^555
xy
xy
xy
xy
=⋅= 55 ⋅
5 24
5 5
36 5 24
3
36
3
==xy
xy
xy
() xy

Roots Expressed as Exponents

Roots can be written as exponents with the following two properties. Rewriting

radical expressions as expressions written to powers is a useful skill in algebra

and especially in calculus.

Property 14 naa= 1/n

The exponent is a fraction whose numerator is 1 and whose denominator is

the root.

EXAMPLE

Rewrite the expression using a fraction exponent.

(^) xx= 12/
(^32121) xx+= +()^13 /
1112 12
x x
==/ x−/
Property 15 naaa
m n m mn
()==/ (If n is even, a must be nonnegative.)
The exponent is a fraction whose numerator is the power and whose denomi-
nator is the root.
EXAMPLES
Rewrite the expression using a fraction exponent.
(^5) xx^3 =^35 /
(^5) xx^6 =^65 /
(^) ()() 2121 xx^27 −=^27 − /^2
EXAMPLE
Rewrite the expression using a fraction exponent.
EXAMPLE
Rewrite the expression using a fraction exponent.
EXAMPLES
Rewrite the expression using a fraction exponent.
EXAMPLES
Rewrite the expression using a fraction exponent.