Fractional Exponents
If n is a positive integer , then
is the
root of a .
If a is positive, it is the positive number b such that
If a is negative, then:
1. If n is odd, is the
negative number b such that
2. If n is even, is undefined.
is also written

Example.
since
is the same as
Note that
is not “±3”.
since
since
is undefined.
Note, however, that
Exp onentiation takes precedence over negation. 
If m and n are positive integers,
means
This makes sense, since
and this should equal
if the rule for multiplying
exponents is to hold in this case.
Equivalently ,
In other words, you can do the root and the power in either order .
involves an n^{th} root, so it may be
positive, negative, or undefined. 
Example.

Example. You can use a calculator to
compute roots and powers. How you do this depends on what kind of
calculator you have. For example,
Roots of negative numbers can present a problem; some calculators will
return a complex number , or
give an error message. You can fix things by figuring out the sign of
the result beforehand. Then make the
base positive for your calculator and fix the sign at the end.
For example, is an odd root of a
negative number, so it’s negative. Knowing this, I use the
calculator to compute
Therefore,
( 
Example. There is some ambiguity here. For
example,
since
But should be undefined, since
I’m taking an even root of a negative number. I will avoid this
problem by always expressing fractional exponents in lowest terms .

The rules I gave earlier for working with integer
exponents work with fractional exponents — with
certain exceptions for even roots.

Example.

Example.

However,
is not the same as x.
Why? and
is always nonnegative. But x could
be negative: For example,
but x = −3.
In this case,
In fact, if n is an even integer,
(Of course, I can drop the absolute values if I know x is nonnegative.) 
Example.

Example. If x and y are nonnegative,

Example.

Example. 
Example. As suming that x and y are
nonnegative ,

Example. 
Start solving your Algebra Problems
in next 5 minutes!




Algebra Helper
Download (and optional CD)
Only $39.99

Click to Buy Now:
OR






2Checkout.com is an authorized reseller
of goods provided by Sofmath


Attention: We are
currently running a special promotional offer
for AlgebraAnswer.com visitors  if you order
Algebra Helper by midnight of
March 24th
you will pay only $39.99
instead of our regular price of $74.99  this is $35 in
savings ! In order to take advantage of this
offer, you need to order by clicking on one of
the buttons on the left, not through our regular
order page.
If you order now you will also receive 30 minute live session from tutor.com for a 1$!

You Will Learn Algebra Better  Guaranteed!
Just take a look how incredibly simple Algebra Helper is:
Step 1
: Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:
Step 2 :
Let Algebra Helper solve it:
Step 3 : Ask for an explanation for the steps you don't understand:
Algebra Helper can solve problems in all the following areas:
 simplification of algebraic expressions (operations
with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots
(radicals), absolute values)
 factoring and expanding expressions
 finding LCM and GCF

(simplifying, rationalizing complex denominators...)
 solving linear, quadratic and many other equations
and inequalities
(including basic logarithmic and exponential equations)
 solving a system of two and three linear equations
(including Cramer's rule)
 graphing curves (lines, parabolas, hyperbolas, circles,
ellipses, equation and inequality solutions)
 graphing general functions
 operations with functions (composition, inverse, range, domain...)
 simplifying logarithms
 basic geometry and trigonometry
(similarity, calculating trig functions, right triangle...)
 arithmetic and other prealgebra topics
(ratios, proportions, measurements...)
ORDER NOW!




Algebra Helper
Download (and optional CD)
Only $39.99

Click to Buy Now:
OR






2Checkout.com is an authorized reseller
of goods provided by Sofmath





"It
really helped me with my homework. I was
stuck on some problems and your software walked me
step by step through the process..." 
C. Sievert, KY
 



Sofmath
19179 Blanco #105234 San Antonio, TX 78258

Phone:
(512) 7885675 Fax: (512) 5191805
  