2. Review: Laws of Exponents

3. Questions Q: 4 0 =? A: 1 Q: 4 1 =? A: 4 Q: 4 1/2 =? A: Let’s square the number (4 1/2 ) 2 =? (4 1/2 ) 2 = 4 1 = 4 Recall: b is called a square root of the number a if b 2 = a. 4 1/2 is a square root of the number 4 Or

4. Definition of Rational Exponent Q: 8 1/3 =? A: Let’s cube the number (8 1/3 ) 3 =? (8 1/3 ) 3 = 8 1 = 8 So, we have In general, for any positive integer n,

5. Examples Evaluate the following expressions

6. Examples Simplify the following expressions

7. Question Which way do you prefer?

8. Definition of Rational Exponent The numerator m will the exponent The denominator n will be the index of the radical 25 3/2 = 3 2

9. Examples 100 7/2 = (-27) 2/3 = 3/2 7 2 2 3 3 2

10. Examples Simplify the following expressions

11. Examples Simplify the following expressions