1. Algebra II Rational Exponents Lesson 6.4
HW: 6.4/10-66 multiples of 3

2. Radicals (also called roots) are directly related to exponents.
Rational Exponents
Radicals (also called roots) are directly related to exponents.
All radicals (roots) can be written in a different format without a radical symbol.
This different format uses a rational (fractional) exponent.

3. Rational Exponents
When the exponent of the radicand (expression under the radical symbol) is one, the rational exponent form of a radical looks like this:
Remember that the index, n, is a whole number equal to or greater than 2.

4. Rational Exponents Examples: base
When a base has a fractional exponent, do not
think of the exponent in the same way as when it is
a whole number.
When a base has a fractional exponent, the
exponent is telling you that you have a radical
written in a different form.

5. Rational Exponents
For any exponent of the radicand, the rational exponent form of a radical looks like this:

6. How do you simplify ? Rational Exponents
Reduce the rational exponent, if possible.
You can rewrite the expression using a radical.
Simplify the radical expression, if possible.
Write your answer in simplest form.

7. Rational Exponents
Example:

8. Rational Exponents
Examples:

9. Rational Exponents
Examples:
No real number solution

10. Rational Exponents
The basic properties for integer exponents also hold for rational exponents as long as the expression represents a real number.

11. Rational Exponents
Example:
What would the answer above be if you were to write it in radical form?

12. Rational Exponents
Example:

13. See the next two slides for a quick review.
Rational Exponents
Do you remember the basic Rules of Exponents that you learned in Roots and Radicals?
See the next two slides for a quick review.

14. The Square Root Rules (Properties)
Rational Exponents
The Square Root Rules (Properties)
Multiplication
Division
b may not be equal to 0.

15. The Cube Root Rules (Properties)
Rational Exponents
The Cube Root Rules (Properties)
Multiplication
Division
b may not be equal to 0.

16. The more general rules for any radical are as follows …
Rational Exponents
The more general rules for any radical are as follows …

17. The Rules (Properties)
Rational Exponents
The Rules (Properties)
Multiplication
Division
b may not be equal to 0.

18. These same rules in rational exponent form are as follows …
Rational Exponents
These same rules in rational exponent form are as follows …

19. The Rules (Properties)
Rational Exponents
The Rules (Properties)
Multiplication
Division
b may not be equal to 0.

20. Rational Exponents
In working with radicals, whether in radical form or in fractional exponent form, simplify wherever and whenever possible.
What is the process for simplifying radical expressions?

21. Rational Exponents
Simplifying radicals – A radical expression is in simplest form once ALL of the following conditions have been met.…
the radicand (expression under the radical symbol) cannot
be written in an exponent form with any factor having an
exponent equal to or larger than the index of the radical;
there is no fraction under the radical symbol;
there is no radical in a denominator.

22. Rational Exponents
Examples – Simplifying Radical Expressions: