1. Warm Up Exercise… Find the range of the function with the given domain (x) – {-2, 0, 3.5}  f(x) = (-2x)(-2x)  g(x) = 10 – (x)(x)(x)  y = 5x – 1

2. Lesson #8.1 Zero & Negative Exponents SWBAT simplify expressions with zero and negative exponents; evaluate exponential expressions. Concept: UNIT 8

3. 2 2 Means… 2 2 = 4 2 1 Means… 2 = 2 2 0 Means… 1 What does 2 -1 Mean? 8.1 – Zero & Negative Exponents

4. What does 2 -1 Mean? You cannot leave an exponent negative because there is NO WAY to express it’s meaning. You must make it positive !

5. You do NOT want to have negative exponents in your answer. You get rid of them by flipping the exponent over, like reciprocals. If the negative exponent is on top, move it to the bottom. 8.1 – Zero & Negative Exponents

6. Definition of Negative Exponent For any integer n, a -n is the reciprocal of a n 8.1 – Zero & Negative Exponents

7. Definition of Negative Exponent For any integer n, a -n is the reciprocal of a n 8.1 – Zero & Negative Exponents

8. Definition of Negative Exponent For any integer n, a -n is the reciprocal of a n 8.1 – Zero & Negative Exponents

9. Simplify. A negative exponent is an inverse! Flip the number over to make the exponent positive! 8.1 – Zero & Negative Exponents

10. Zero Exponent: Negative Exponent: NEVER RULE: YOU SHOULD NEVER HAVE A NEGATIVE EXPONENT AS YOUR FINAL ANSWER 8.1 – Zero & Negative Exponents

11. Simplify. 8.1 – Zero & Negative Exponents

12. Simplify the following: a. 3c. (-4) b. (-8.1)d. (2.45678913) -2 -5 0 0

13. Simplify. 8.1 – Zero & Negative Exponents

14. Simplify a. 11mb. 7s - 4t c. d. -5 2

15. Simplify the following expressions: 1 x5x5 16 -n3p6-n3p6 1

16. Practice Problems 1. 2 -2 ¼ 2. (-2) 0 1 3. 5 -x 1/5 x 4. (½) -1 2 5. 5(2 -1 ) 5/2 6. 2x -2 y -3 2/y 3 x 2

17. More Practice 7. x -5 1/x 5 8. x 5 /2 9. x 4 y -7 x 4 /y 7 10. x 3 y/9

18. 8.1 – Zero & Negative Exponents Evaluate each expression for n = -2 and w = 5 a. n wb. c. d. -30