1. Objectives: Students will be able to… Use properties of rational exponents to evaluate and simplify expressions Use properties of rational exponents to evaluate and simplify expressions

2.  Examples: THE PROPERTIES OF EXPONENTS WE LEARNED IN SECTION 6.1 ARE THE SAME FOR RATIONAL EXPONENTS!!!

3.  Simplify:

4.  1. 2. Using Properties of Radicals to Simplify

5.  1. 2. For a radical to be in simplest form, you must remove any perfect n th powers (other than 1) and rationalize any denominators Multiply top and bottom by a quantity that will make the denominator a perfect 4 th power.

6.  1. 2. Write in simplest form.

7.   Can only add or subtract radical expressions if they are like radicals (just like combining like terms!!)  Examples: 1.) 2.) Like Radicals : same index, same radicand

8.  1. 2. You try…Perform indicated operation

9.   Rewrite radicand so exponents match index, if possible  Take out any expressions that match the index  Can apply any rule of exponents Simplifying Radicals with Variables (assume all variables positive)

10.  Examples: Simplify

11.  Write the expression in simplest form. Make denominator perfect 5 th root…multiply by h 3 on top and bottom

12.  You try!! Simplify

13.  Challenge…Simplify

14.   Perform indicated operation. Assume all variables positive. To add or subtract radical expressions involving variables, you also need like radicals (may need to simplify first!!) NOT LIKE RADICALS!!

15.  You try…perform indicated operation.