1. 13.4
Rational Exponents

2. Understanding a1/n Recall that a cube root is defined so that
However, if we let b = a1/3, then
Since both values of b give us the same a,
If n is a positive integer greater than 1 and is a real number, then

3. Example
Use radical notation to write the following. Simplify if possible. a. b. c.

4. Understanding am/n as long as is a real number
If m and n are positive integers greater than 1 with m/n in lowest terms, then
as long as is a real number

5. Example
Use radical notation to write the following. Simplify if possible. a. b.

6. Understanding am/n
as long as a-m/n is a nonzero real number.

7. Example
Use radical notation to write the following. Simplify if possible. a. b.

8. Example
Use properties of exponents to simplify the following. Write results with only positive exponents. a.