1. 6.1 Nth Roots and Rational Exponents
Objectives:
How do you change a power to rational form and vice versa?
How do you evaluate radicals and powers with rational exponents?
How do you solve equations involving radicals and powers with rational exponents?

2. Concept: Knowing the Parts
The index number becomes the denominator of the exponent.
Index Number
Radical
for n > 1
Radicand
Exponent
The exponent becomes the numerator in Exponential Form

3. Concept: Radicals If n is odd, then there is one real root.
If n is even and
a > 0 there are two real roots
a = 0 there is one real root
a < 0 there are no real roots
This is EXACTLY the same as the discriminate we
looked at when we used the Quadratic Formula.

4. Concept: Radical form to Exponential Form
Change to exponential form.

5. Concept: Exponential to Radical Form
Change to radical form.
The numerator of the exponent becomes the exponent of the radicand.
The denominator of the exponent becomes the index number of the radical.

6. Concept: Evaluate With a Calculator
Rewrite in Exponential Form.
2. Type into calculator

7. PM 6.1

8. Concept: Solving an equation
Solve the equation:
_______________________
Note: index number is even, therefore, two answers.

9. Concept: Rules
Rational exponents and radicals follow the properties of exponents.
Also, Product property for radicals
Quotient property for radicals

10. Example: Using the Quotient Property
Simplify.

11. Concept: Adding and Subtracting Radicals
Two radicals are like radicals, if they have the same index number and radicand
Example
Addition and subtraction is done with like radicals.

12. Example: Addition with like radicals
Simplify.
Note: same index number and same radicand.
Add the coefficients.

13. Example: Subtraction Simplify.
Note: The radicands are not the same. Check to see if we can change one or both to the same radicand.
Note: The radicands are the same. Subtract coefficients.