By: Catalina Arredondo, Willy Metellus, and Matt Delaney

A rational exponent is in other words a “fractional exponent”. Where problems are rewritten and solved using a unique relationship with fractions, radicals, and exponents.

Where the root becomes the power

The root of the radical ends up becoming the base numbers exponent over one.

As in √A = A1/2

Index Numbers An index number is the number directly to

the left of a radical sign The index number indicates the root you are

taking of the number within the radical

For Example… ∛8 = 2, because 2*2*2=8

∜81 = 3, because 3*3*3*3=81

•Square root can be written as a half power√4 = 41/2

•Third root can be written as one-third∛8 = 81/3

•Fourth root can be written as one-fourth root∜81 = 811/4

And so on …

1.) Product Rule(add exponent)

2.)Quotient Rule(when dividing by same base subtract

exponents)

3.)Power to Power Rule(multiply exponents)

4.)Product to a Power Rule(Distribute exponent to each base)

5.)Fraction to a Power Rule(Distribute exponent in the fraction)

6.)Negative Exponent Rule(change the negative sign in the

exponent and put the whole problem over one do it will become a fraction)

1. A3 x A3 = A6

2. A6 /A3 = A3

3. (A3) 2 = A6 4. (AB)2 = A2 B2

5. (A/B)2 = A2/B2

6. A-2 = 1/A2

(5^2)^4 Problem

5^8 Multiply Exponents

390,625 Simplify

5^5 / 5^3 Problem

5^2 Subtract Exponents

25 Simplify

(6x5)^2 Problem

6^2 X 5^2 Distribute Exponent

36 x 25 Multiply 900 Simplify

http://www.youtube.com/watch?v=k_ezKATh7Hc

this video explains rational exponents: what they are, what they

mean, and how to interpret them.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut5_ratexp.htm

pretty much all of the information you could need regarding rational exponents. within the page it has a yellow box with

all of the rules.

http://www.regentsprep.org/Regents/math/algtrig/ATO1/FractionalExp.htm

Similar to the link above with helpful info