1. December 15, 2010 WECHS 10th Grade Math
Rational Exponents
December 15, 2010
WECHS 10th Grade Math

2. Rational Exponents Ex: ⅓,⅗,⅝ Ex: x ⅓, y ⅗, z ⅝
Remember, a rational number is one that can be written as a fraction.
Ex: ⅓,⅗,⅝
So a rational exponent is a fraction in the exponent:
Ex: x ⅓, y ⅗, z ⅝

3. Different Forms
The following rule can be used when working with a fractional, or rational, exponent: The denominator is the root; the numerator is the power. It does not matter what order you do the operations in – the equation is true whether you take the root or raise the power first.

4. Example
Write in root form, and evaluate it.

5. Example 2
Write in root form, and evaluate it. It’s usually easiest to take the root first:

6. Example 3
Simplify First, Convert to root form:

7. Solving an equation
If x has a rational exponent, get it into the form:
Get rid of the root by raising it to the mth power. Then take the nth root.

8. Solving an equation - Example
Solve for x:
Get rid of the root by raising it to the mth power. Then take the nth root.