Rational Exponents MATH 017 Intermediate Algebra S. Rook

2 Overview Section 7.2 in the textbook –Simplify rational exponents –Apply rational exponents to simplify rational expressions

Simplify Rational Exponents

4 Rational Exponents Thus far, we have only seen integer exponents –Ex: 5 3, x -5 Possible to have rational (i.e. fractional) exponents –Ex: 8 1/3, y -3/4

5 Rational Exponents vs Radical Notation Relationship between rational exponents and radical notation where p is power and r is radical Ex: Most calculators take only up to the third root –How would we evaluate

6 Rational Exponents vs Radical Notation (Example) Ex 1: Use radical notation to write the following and simplify if possible

7 Rational Exponents vs Radical Notation (Example) Ex 2: Use radical notation to write the following and simplify if possible

8 Negative Rational Exponents Write any negative rational exponents as positive rational exponents Apply radical notation and simplify if possible

9 Rational Exponents vs Radical Notation (Example) Ex 3: Use radical notation to write the following and simplify if possible. Leave NO negative exponents

Simplify Rational Exponent Expressions

11 Simplify Rational Exponent Expressions Exponent rules for integer exponents apply to rational exponents as well –Remember them? Product: x a ∙ x b = x a+b Quotient: x a / x b = x a-b Power: (x a ) b = x ab

12 Simplify Rational Exponent Expressions (Example) Ex 4: Use the properties of exponents to simplify – write with only positive exponents

13 Simplify Rational Exponent Expressions (Example) Ex 5: Use the properties of exponents to simplify – write with only positive exponents

14 Simplify Rational Exponent Expressions (Example) Ex 6: Use the properties of exponents to simplify – write with only positive exponents

15 Simplify Rational Exponent Expressions (Example) Ex 7: Use the properties of exponents to simplify – write with only positive exponents

16 Simplify Rational Exponent Expressions (Example) Ex 8: Use rational exponents to simplify the following – leave the final answer in radical notation

17 Summary After studying these slides, you should know how to do the following: –Understand rational exponents. This includes being able to convert to radical notation and simplify –Simplify expressions containing rational expressions using the exponent rules