Algebra Demystified 2nd Ed

Chapter 5 e X P O N e N T S a N D r O O T S 127

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

TABLE 51

Exponent Properties Root Properties Roots Expressed as Exponents

aamn=amn+ nnab= abn^ naa= 1/n

a

a

a

m

n

= mn− a

b

a

b

n

n

=n

naam= mn/

()aamn= mn (naa)m=n m

If n is even, a ≥ 0

naa

m mn

( ) = /

If n is even, a ≥ 0

a^0 = (^1) (naa)n==n n a
If n is even, a ≥ 0
a
a
n
n
− =^1
()abnn=abn
a
b
a
b
m m
m



 =
a
b
b
a
n n
n



 =
−

Summary

In this chapter, we learned how to use the exponent and root properties below

to simplify and rewrite expressions.

We also learned how to

• Find the LCD of fractions whose denominators contained exponents. The LCD
  includes expressions raised to the highest power in each denominator.


• Simplify square roots. If the quantity under that radical is the product of a
  square and something else, the square root can be simplified with the
  properties nnab= abn and naan=.


• Rationalize a denominator. If the denominator includes a square root as a
  factor, we multiply the numerator and denominator by this factor. This
  removes the square root from the denominator because of the property
  ( aa) =

2

..

We will use exponent and root properties later when solving some equations.