1. Zero and Negative Exponents © 2006, Mr. C. Burke. All rights reserved.

2. Review: Adding and Subtracting Exponents  If you multiply two terms that have the same base value, you add the exponents. x 3 * x 6 = x 9 If you divide two terms that have the same base value, you subtract the exponents. x 8 / x 6 = x 2

3. Review: Multiplying Exponents  If you have a variable that has more than one exponent, you multiply the exponents. (a 3 ) 2 = a 3 * a 3 = a 3*2 = a 6 (b 2 ) 3 = b 2 * b 2 * b 2 = b 2*3 = b 6

4. Review: Multiplying Exponents  Use the Distributive Property if you have more than one variable inside the parentheses: (ab) 2 = a * a * b * b = a 2 b 2 (5c 4 ) 2 = 5 * 5 * c 4 * c 4 = 25b 8 (mc 2 ) 3 = m * m * m * c 2 * c 2 * c 2 = m 3 c 6

5. Review: Multiplying Exponents  Try these examples in your notebooks: (xy) 2 = _____________ (jk 3 ) 3 = _____________ (abc) 4 = ______________

6. Review: Multiplying Exponents  Compare your answers. How did you do? (xy) 2 = x * x * y * y = x 2 y 2 (jk 3 ) 3 = j * j* j * k 3 * k 3 * k 3 = j 8 k 8 (abc) 4 = a * a * a* a* b* b* b* b * c * c * c = a 4 b 4 c 4

7. Zero Exponents  Anything divided by itself is one. (1) 5mn 2 However, we said that when we divide, we subtract exponents, so n 2 / n 2 = n 2 – 2 = n 0 ANY NUMBER OR EXPRESSION WITH AN EXPONENT OF ZERO has the value of 1.

8. Negative Exponents Look at the chart below: 5 3 = 5 * 5 * 5 = 125 5 2 = 5 * 5 = 25 (5 3 divided by 5) 5 1 = 5 = 5 (5 2 divided by 5) As we divide by 5, the exponent goes down by 1. What happens if we keep this pattern going?

9. Negative Exponents Look at the chart below: 5 3 = 5 * 5 * 5 = 125 5 2 = 5 * 5 = 25 5 1 = 5 = 5 5 0 = 1 = 1 5 -1 = 1 / 5 = 1 / 5 5 -2 = 1/ 5 * 1/ 5 = 1 / 25 5 -3 = 1/ 5 * 1/ 5 * 1/ 5= 1 / 125

10. Negative Exponents Look at the pattern: 1 1 1 1 5 -3 = n -4 = 5 3 n 4 5 3 n 4 Rewrite these expressions without negative exponents: n -3 m -4 p 3 q -2 j –3 k –4

11. Homework Page 382, #1-5, #20-24 Please COPY the question and write the answer on your loose leaf paper. Write each expression as an integer or simple fraction. -2.57 0 4 -2 (-5) -1 (2/3) -1 1/ 2 -3 Write each expression so that it contains only positive exponents. 1/c -1 1/x -7 3ab 0 (5x) -4 5 -2 /p