1. Number Systems-Part 8

2. Radicals with Variables
The same rules can be applied to variable expressions as well. You can either look for groups by expanding, or look for the variable exponent to match the index. If the exponent and index match, the variable moves outside of the radical symbol.

3. Examples

4. More Examples
We can apply the rules to simplify radical expressions that have both integers and variables.

5. Even More Examples!
Or in more challenging problems, we can use power rules and radical rules to simplify.

6. Why do the Radical Rules Work?
We already discussed that roots and exponents are related. The appropriate root will “undo” an exponent, and the right exponent will “undo” a root.

7. Roots as Powers
When you write roots as exponents, the power under the radical symbol becomes the numerator for the exponent, and the index becomes the denominator.