1. Section 1.2 Exponents & Radicals
Objectives:
To review exponent rules
To review radicals
To review rational exponents

2. Integer Exponents an = a · a · · · · · a
The number a is called the base and n is called the exponent.

3. Ex 1. Simplify

4. Zero & Negative Exponents
If a ≠ 0 is any real number and n is a positive integer, then a0 = 1 and a–n =

5. Ex 2. Simplify 1

6. Laws of Exponents
Law Example 1) 2) 3) 4) 5)

7. Class Work
Simplify

8. Laws for Negative Exponents
Law Example 6. 7.

9. Ex 3 Simplify
a) b)

10. Class Work
6. 7.

11. Radicals
The symbol √ means: “the positive square root of.”
Thus,

12. nth Roots If 24 = 16, then it follows that .
If n is any positive integer, then the principal nth root of a is defined as follows:
If n is even, we must have a ≥ 0 and b ≥ 0.

13. Ex 4. Simplify
a) b) c) d)

14. Properties of nth Roots
Property Example

15. Property Example 4. 5.

16. Ex 5. Simplify

17. Class Work

18. Rational Exponents
For example, and,

19. Ex 6. Simplify

20. Class Work