1. Lesson 8-1 Negative & Zero

2. Your Goal: Simplify expressions containing integer exponents.

3. Zero Power The zero power of any number except 0 equals 1. 100 = 1 0 (-5) = 1 0

4. 24 0 19 0 Now You Try: Evaluate. 1. 10 0 2. 175 0 3. 10,347 0 4. All the answers are 1!

5. Negative Exponents Any number or variable (except 0) with a negative exponent means move that number or variable to the opposite place of the fraction. 5 = ( ) 1 5 3 -3

6. 1. 5 –3 Evaluating Negative Exponents 1 5 5 5 = 125 1 = The 5 has a negative exponent so move it from the top of the fraction to the bottom.

7. 2. (–10) –3 Evaluating Negative Exponents Evaluate. 1 –10 –10 –10 = –1000 1 = OR –0.001 The -10 has a negative exponent so move it from the top of the fraction to the bottom.

8. 3. 4 –2 Try this one: Evaluate. 1 4 = 16 1 = The 4 has a negative exponent so move it from the top of the fraction to the bottom.

9. Subtract inside the parentheses. 5. Evaluate 5 – (6 – 4) –3 + (– 2) 0. Evaluate the exponents. Don’t forget the Order of Operations!!! 5 – (6 – 4) –3 + (–2) 0 = 5 – (2) –3 + (–2) 0 = 5 – + 1 1818 = 5 7878 Add and subtract from left to right.

10. 6. Evaluate 5x –4 How would you solve this one? Only move what is attached to the exponent. Leave anything NOT attached to the exponent alone. 5 x 4 = The x has a negative exponent so move it from the top of the fraction to the bottom.

11. 7. Evaluate 1/x –3 How would you solve this one? x3x3 = The x has a negative exponent so move it from the bottom of the fraction to the top.

12. Now You Try: Evaluate. 8. 9. 10. 8. 9. 3x 2 10.

13. Negative Exponents (MOVE IT MOVE IT!): Any number except 0 with a negative exponent equals its reciprocal with the opposite exponent (If it’s on top, put it on bottom of the fraction. If it’s on bottom, put it on top of the fraction.) Zero Power: The zero power of any number except 0 equals 1.

14. REMEMBER Your goal is to learn how to simplify expressions containing integer exponents! Let’s see how you do!