Rational Exponents

1. Intermediate Algebra -MTH04 Rational Exponents Mr. Joyner Tidewater Community College

2. Intermediate Algebra MTH04 Rational Exponents Radicals (also called roots) are directly related to exponents.

3. Intermediate Algebra MTH04 Rational Exponents All radicals (roots) can be written in a different format without a radical symbol.

4. Intermediate Algebra MTH04 Rational Exponents This different format uses a rational (fractional) exponent.

5. Intermediate Algebra MTH04 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.

6. base Intermediate Algebra MTH04 Rational Exponents Examples: • 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.

7. Intermediate Algebra MTH04 Rational Exponents For any exponent of the radicand, the rational exponent form of a radical looks like this:

8. Intermediate Algebra MTH04 Rational Exponents How do you simplify ? • 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.

9. Intermediate Algebra MTH04 Rational Exponents Example:

10. Intermediate Algebra MTH04 Rational Exponents Examples:

11. Intermediate Algebra MTH04 Rational Exponents Examples: No real number solution

12. Intermediate Algebra MTH04 Rational Exponents The basic properties for integer exponents also hold for rational exponents as long as the expression represents a real number. See the chart on page 389 of your text.

13. Intermediate Algebra MTH04 Rational Exponents Example: What would the answer above be if you were to write it in radical form?

14. Intermediate Algebra MTH04 Rational Exponents Example:

15. Intermediate Algebra MTH04 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.

16. Intermediate Algebra MTH04 Rational Exponents The Square Root Rules (Properties) Multiplication Division b may not be equal to 0.

17. Intermediate Algebra MTH04 Rational Exponents The Cube Root Rules (Properties) Multiplication Division b may not be equal to 0.

18. Intermediate Algebra MTH04 Rational Exponents The more general rules for any radical are as follows …

19. Intermediate Algebra MTH04 Rational Exponents The Rules (Properties) Multiplication Division b may not be equal to 0.

20. Intermediate Algebra MTH04 Rational Exponents These same rules in rational exponent form are as follows …

21. Intermediate Algebra MTH04 Rational Exponents The Rules (Properties) Multiplication Division b may not be equal to 0.

22. Intermediate Algebra MTH04 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?

23. Intermediate Algebra MTH04 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.

24. Intermediate Algebra MTH04 Rational Exponents Examples – Simplifying Radical Expressions: