Your Ad Here

Please study  the Basics of Fractional Exponents,
if you have not already done so.

It is a prerequisite here.

There, we provided the explanation for Rational Exponents.

We applied the same 7 Laws and the 2 Rules
in solving problems for Rational Exponents.

We provided a few solved examples
and problems for practice with answers.

Here we provide many more Solved
Examples and Exercises with answers.

Studying the worked out problems will help remember and
apply the 7 Laws and the 2 Rules for Rational Exponents.

Practice makes one perfect.

This is especially true for remembering
Algebra Formulas (Math Formulas).

So, take the exercises seriously
and practice solving the problems.

Get The Best Grades With the Least Amount of Effort : Fractional Exponents

Here is a collection of proven tips,
tools and techniques to turn you into
a super-achiever - even if you've never
thought of yourself as a "gifted" student.

The secrets will help you absorb, digest
and remember large chunks of information
quickly and easily so you get the best grades
with the least amount of effort.

If you apply what you read from the above
collection, you can achieve best grades without
giving up your fun, such as TV, surfing the net,
playing video games or going out with friends!

Know more about the Speed Study System.

Set of Solved Examples : Fractional Exponents

Solved Example 1 of Fractional Exponents

If ax = by = cz and ba = cb, show that yx = 2z⁄(x + z)

Solution to Example 1 of Fractional Exponents:

Let ax = by = cz = k
a = k1⁄x; b = k1⁄y; c = k1⁄z;
By data, ba = cb ⇒ (k1⁄y)⁄(k1⁄x) = (k1⁄z)⁄(k1⁄y)
We know aman = am - n
Applying this here, we get
(k1⁄y - 1⁄x) = (k1⁄z - 1⁄y)
Since the bases are same, the exponents have to be equal.
∴ (1⁄y - 1⁄x) = (1⁄z - 1⁄y)
⇒ 1⁄y + 1⁄y = 1⁄z + 1⁄x ⇒ 2⁄y = (x + z)⁄xz
Multiplying both sides with x⁄2, we get
xy = (x + z)⁄2zyx = 2z ⁄(x + z) (Proved.)


src="" alt="Great deals on

School & Homeschool Curriculum Books and Software" width="468" height="60">

Solved Example 2 of Fractional Exponents

If y = 31⁄3 + 1⁄(31⁄3), show that 3y3 - 9y = 10.

Solution to Example 2 of Fractional Exponents:

Let a = 31⁄3. Then a3 = 3........(i)
and b = 1⁄(31⁄3). Then b3 = 1⁄3 .......(ii)
Also, ab = 1.......(iii) and a + b = y........(iv).
y = 31⁄3 + 1⁄(31⁄3) = a + b
y3 = (a + b)3 = a3 + b3 + 3ab(a + b)
Using (i), (ii), (iii) and (iv) here, we get
y3 = 3 + 1⁄3 + 3(1)(y)
Multiplying both sides with 3, we get
3y3 = 9 + 1 + 9y ⇒ 3y3 - 9y = 10. (Proved.)

Target="_Top">Great Deals on School & Homeschool Curriculum Books

src="" width="1" height="1">

Solved Example 3 of Fractional Exponents

Solve 2x1⁄3 + 2x-1⁄3 = 5.

Solution to Example 3 of Fractional Exponents:

Let a = x1⁄3. Then x-1⁄3 = 1⁄a.
The given equation becomes 2a + 2⁄a = 5.
Multiplying both sides with a, we get
2a2 + 2 = 5a. ⇒ 2a2 - 5a + 2 = 0.
This is a quadratic equation.
We know

The solution of the quadratic equation ax2 + bx + c = 0 is
x = {-b ± √( b2 - 4ac) }⁄2a

Applying this here, we get
a = [-(-5) ± √{(-5)2 - 4(2)(2)}]⁄[2(2)]
= [5 ± √{ 25 - 16 }]⁄[4] = [5 ± √{ 9 }]⁄[4] = [5 ± 3]⁄[4]
= (5 + 3)⁄4 or (5 - 3)⁄4 = 8⁄4 or 2⁄4 = 2 or 1⁄2 .
a = x1⁄3a3 = x;
x = 23 or (1⁄2)3 = 8 or 1⁄8. Ans.

Progressive Learning of Math : Fractional Exponents

Recently, I have found a series of math curricula
(Both Hard Copy and Digital Copy) developed by a Lady Teacher
who taught everyone from Pre-K students to doctoral students
and who is a Ph.D. in Mathematics Education.

This series is very different and advantageous
over many of the traditional books available.
These give students tools that other books do not.
Other books just give practice.
These teach students “tricks” and new ways to think.

These build a student’s new knowledge of concepts
from their existing knowledge.
These provide many pages of practice that gradually
increases in difficulty and provide constant review.

These also provide teachers and parents with lessons
on how to work with the child on the concepts.

The series is low to reasonably priced and include

Elementary Math curriculum


Algebra Curriculum.

Exercise on Fractional Exponents

  1. Show that
    1⁄(1 + xa - b + xa - c) + 1⁄(1 + xb - c + xb - a) + 1⁄(1 + xc - a + xc - b) = 1.
  2. If ax = by = cz = dw and ab = cd,
    show that: 1⁄x + 1⁄y = 1⁄w + 1⁄z .
  3. If a1⁄3 + b1⁄3 + c1⁄3 = 0, show that: (a + b + c)3 = 27abc.

For Answers, see at the bottom of the page.

Answers to Exercise on Fractional Exponents

  1. (i) 1. (ii) 1.
  2. (i) 1⁄2. (ii) -8.

Research-based personalized
Math Help tutoring program :
Fractional Exponents

Here is a resource for Solid Foundation in
Math Fundamentals from Middle thru High School.
You can check your self by the


Are you spending lot of money for math tutors to your
child and still not satisfied with his/her grades ?

Do you feel that more time from the tutor and
more personalized Math Help to identify and fix
the problems faced by your child will help ?

Here is a fool proof solution I strongly recommend
and that too With a minuscule fraction of the amount
you spent on tutors with unconditional 100% money
back Guarantee, if you are not satisfied.


It is like having an unlimited time from an excellent Tutor.

It is an Internet-based math tutoring software program
that identifies exactly where your child needs help and
then creates a personal instruction plan tailored to your
child’s specific needs.

If your child can use a computer and access
the Internet, he or she can use the program.
And your child can access the program anytime
from any computer with Internet access.

Unique program to help improve math skills quickly and painlessly.

There is an exclusive, Parent Information Page provides YOU
with detailed reports of your child’s progress so you can
monitor your child’s success and give them encouragement.
These Reports include

  • Time spent using the program
  • Assessment results
  • Personalized remediation curriculum designed for your child
  • Details the areas of weakness where your child needs additional help
  • Provides the REASONS WHY your child missed a concept
  • List of modules accessed and amount of time spent in each module
  • Quiz results
  • Creates reports that can be printed and used to discuss issues with your child’s teachers
These reports are created and stored in a secure section
of the program, available exclusively to you, the parent.
The section is accessed by a password that YOU create and use.
No unauthorized users can access this information.

Personalized remediation curriculum designed for your child

Thus The features of this excellent Tutoring program are

  • Using detailed testing techniques
  • Identifing exactly where a student needs help.
  • Its unique, smart system pinpointing precise problem areas -
  • slowly and methodically guiding the student
  • raising to the necessary levels to fix the problem.

Not a “one-size-fits-all” approach!

Its research-based results have proven that
it really works for all students! in improving
math skills and a TWO LETTER GRADE INCREASE in
math test scores!,if they invest time in using
the program.

Proven for More than 10,000 U.S. public school
students who increased their math scores.

Proven methodology!