1. Fractional Exponents

2. Careful! Calculate the following in your calculator: 2 ^ ( 1 ÷ 2 ) Not Exact

3. A Math Trick to Evaluate 2 ½ Exactly Evaluate the following using our rules: 2 1/2. 2 1/2 2 1/2 + 1/2 2121 2

4. What Does 2 ½ Exactly Equal? The final answer makes sense because: What is the number whose square is 2: x 2 = 2 ?

5. Irrational Numbers Radical numbers/Fractional Roots are typically irrational numbers (unless they simplify to an integer). Our calculator gives: But the decimal will go on forever because it is an irrational number. For the exact answer just use:

6. More Fractional Exponents Change the following into a radical: 2 1/3 = Remember 2 1/2 is also called the square root of 2 The cube root of 2. The solution to x 3 = 2

7. n th Roots The n th root of a number x is a number r which, when multiplied by itself n times equals x. Examples:

8. Radical v. Exponential Notation Rewrite the following roots as an exponential expression:

9. Square Root Notation Remember: The 2 is implied!

10. Roots in the Calculator (6)(12) MATH 12^(1÷6) Exponential Notation: Radical Notation: is found in #5

11. What Does 2 5/3 Exactly Equal? 2 5/3 ≈

12. Exponents into Radical Notation b p/q = Generally b≥0

13. Example Evaluate the following without a calculator: