

Simplify Fraction ExponentsFormula and examples of how to simplify Fraction exponentsSimplify Rational Expressions worksheet (Free pdf with answer key on this page's topic: how to simplify fractional exponents) This Page: formula for fraction exponents  formula fraction exponent: numerator not one
If you have ever calculated the square root of a number then you were actually using a fraction exponent! The square root of a number is the same as raising that number to an exponent of ½
What about other fractions in the exponent?
To try to understand the idea behind fraction exponents let's examine a property of the fractional exponents. The math below comes directly from the basic laws of exponents. So we all know that the square root of 9 (or 9^{½}) is three and that 3*3 = 9, right? Well, what about the next lines? What about 8^{1/3}? 8^{1/3} is another way of asking: "What can you multiply by itself three times to get 8?"What number is that? The number 2! Remember 2*2*2 = 8. Therefore, 8^{1/3} = 2 . By the same logic we can determine that 81 ^{¼} is the number 3(3*3*3*3 = 81). 8^{¼} is another way of asking: "What number can you multiply by itself four times to get 8?" General Formula for fractional exponentsI want to point out that we have only been dealing with fractional exponents with a numerator of 1! Later on we will deal with fractional exponents with other numerators Below is the general formula for a fractional exponent with a numerator of x^{1/n} is another way of asking: "What number can you multiply by itself n times to get x?" Practice Problems with fracitonal exponents whose numerator is 1Simplify each fraction exponent
Simplify 125^{1/3}
Formula when the fraction in the exponent is not oneBelow is a specific example illustrating the formula for fraction exponents when the numerator is not one. There are two ways to simplify a fraction exponent such 2/3. You can either apply the numerator first or the denominator. See the example below.
Simplify 125^{2/3}
Simplify 64^{2/3}
Simply 81¾
