1. Exponent Laws MHF4UI Friday October 12 th, 2012

2. How much do you remember from Grade 9? 1)7 1 2)Z 0 3)3 -3 4)4 -7 × 4 5 5)2 -3 ÷2 -6 6) (2 5 )⁴ 7) (2xy) 3 8) (5/4) 2 9) 4 3/2 10) (a 3 b 1 c 0 ) -2/3

3. ANSWER KEY 1)7 2)1 3)1/27 4)1/16 5)8

4. Exponent Law #1 x 1 = x Examples: 7 1 =7 s 1 = s

5. Exponent Law #2 x 0 = 1 Examples: 18 0 =1 z 0 = 1

6. Exponent Law #3 x -1 = 1/x This is called the Reciprocal of x Examples: 4 -1 = 1/4

7. Exponent Law #3 (Continued) x -n = 1/x n = (1/x) n Examples: 3 -3 = 1/3 3 = 1/27 (5/4) -2 = (4/5) 2 = 16/25 k -2 = 1/k 2

8. Exponent Law #4 x n ● x m = x (n+m) x 2 x 3 = (xx)(xxx) = xxxxx = x 5 Examples: 2 2 × 2 3 = 2 (2+3) = 2 5 = 32 4 -7 × 4 5 =4 (-7+5) = 4 -2 = 1/16 y 5 ● y -2 = y (5-2) = y 3

9. Exponent Law #5 x n ÷ x m = x (n-m) x 4 /x 2 = (xxxx) / (xx) = xx = x 2 Examples: 2 2 ÷ 2 4 = 2 (2-4) = 2 -2 = 1/4 2 -3 ÷2 -6 =2 (-3-(-6)) = 2 3 = 8 t 5 ÷ t -2 = t (5-(-2)) = t 7 x 2 /x 2 = x 2-2 = x 0 =1

10. Exponent Law #6 (x n ) m = x nm (x 2 ) 4 = (xx) 4 = (xx)(xx)(xx)(xx) = xxxxxxxx = x 8 Examples: (3 2 ) 3 = 3 6 (2 5 )⁴ = 2 20

11. Exponent Law #7 (xy) n = x n y n (xy) 3 = (xy)(xy)(xy) = xyxyxy = xxxyyy = (xxx)(yyy) = x 3 y 3 Examples: (2xy) 3 = 2 3 x 3 y 3 = 8x 3 y 3

12. Exponent Law #8 (x/y) n = x n /y n (x/y) 3 = (x/y)(x/y)(x/y) = (xxx)/(yyy) = x 3 /y 3 Examples: (5/4) 2 = 5 2 /4 2 = 25/16

13. Exponent Law #9

14. Some Trickier Examples:

15. Exponent Law #10 The only way to learn your exponent laws is to practice! Homework: Exponent Law Worksheet