1. copyright©amberpasillas2010 An exponent tells how many times a number is multiplied by itself. 8 3 Base Exponent #1 Factored Form 3 3 a a a Exponential Form 3 2 a 3 x y x 2 2x 2 y 1 888= 512

2. copyright©amberpasillas2010 # 2 When s implifying exponents you must watch the sign and the p arenthesis ! 52 52 = 5 5 = 25 –5 2 = –5 5 = –25 (-5) 2 = (-5) ( -5) = 25 –(5) 2 = - (5) ( 5) = –25 1 copyright©amberpasillas2010

3. Evaluate The Power #3 1) 2) 3) 4) To find 5 on my calculator I type in 4 54 ^ = 625 5 yxyx 4 Try to find 9 = 729 3 copyright©amberpasillas2010

4. Powers of Ten 2 10 3 4 5 100 1,000 10,000 100,000 1010 1 10 1 10 = 0.1 # 4 10 -2 1 1 10 2 1 100 = 0.01 10 -3 1 10 3 1 1000 = 0.001

5. copyright©amberpasillas2010 Negative Exponents # 5 EXAMPLES: For any integer n, a -n is the reciprocal of a n A negative exponent is an inverse!

6. copyright©amberpasillas2010 Any number to the zero power is ALWAYS ONE. x 0 = 1 Ex: # 6

7. copyright©amberpasillas2010 Exponents and Parenthesis #7 Factored Form 8 x x x Exponential Form 8x 3 4(xy)(xy) 4(xy) 2 (8x) 3 (8x)(8x)(8x) = 8 3 x 3 = 4 x 2 y 2 (5x 3 ) 2 (5 x x x)(5 x x x) = 25x 6 (2y 2 z) 2 (2 y y z) (2 y y z) = 2 2 y 4 z 2 = 512x 3 = 5 2 (x 3 ) 2 = 4y 4 z 2

8. copyright©amberpasillas2010 Fractions With Exponents # 8

9. copyright©amberpasillas2010 Negative Exponent Examples # 9

10. copyright©amberpasillas2010 Just flip the fraction over to make the exponent positive ! #10

11. copyright©amberpasillas2010 When multiplying powers with the same base, just ADD the exponents. For all positive integers m and n: a m a n = a m + n Ex : #11 (3 2 )(3 3 ) = (3 3) (3 3 3) = 3 2+3 = 3535 (x 5 )(x 4 ) = x 5+4 = x 9

12. copyright©amberpasillas2010 To find the power of a power, you MULTIPLY the exponents. This is used when an exponent is on the outside of parenthesis. # 12 = 5 3 a 2 3 b 3 (5 1 a 2 b) 3 (2 1 x 3 ) 5 = 2 5 x 3 5 8(3 1 y 8 z) 2 = 8 ( 3 2 y 8 2 z 2 ) = 125a 6 b 3 = 32x 15 = 72 y 16 z 2

13. copyright©amberpasillas2010 #13 = x 8+5 x 8 x 5 (4a 7 b) 3 = 4 3 a 7 3 b 3 = x 13 = 64 a 21 b 3 Product of a Power Property Power of a Power Property = (-12) 2 (-3 4) 2 =144 Power of a Product Property = (-12)(-12)

14. copyright©amberpasillas2010 Prime Factorization is when you write a number as the product of prime numbers.  Factor Tree 36 #14 2 18 2 9 3 3 Circle the prime numbers

15. copyright©amberpasillas2010 Factoring #15 1) == 2) == 12 2 6 2 3

16. copyright©amberpasillas2010 # 16 When Dividing Powers with the same base, just SUBTRACT THE EXPONENTS. This is called the Quotient of Powers Property. x 5 x 2 == x 5 x 2 = or

17. copyright©amberpasillas2010 #17

18. copyright©amberpasillas2010 COEFFICIENT: The number in front of the variable is the coefficient. Multiply coefficients. Add exponents if the bases are the same # 18 1) 2)

19. copyright©amberpasillas2010 # 19 Dividing Powers With Negatives Quotient of Powers Property x a x b = = = == ==

20. copyright©amberpasillas2010 #20 Simplify.

21. copyright©amberpasillas2010 # 21 Quotient of Powers Property Quotient of Powers Property x a x b = Same

22. copyright©amberpasillas2010 Extras

23. copyright©amberpasillas2010 Exponents & Powers An exponent or power tells how many times a number is multiplied by itself. 3 4 Base Exponent #1 “Five to the 2nd power” “Five squared” “Seven to the 3rd power” “Seven cubed”

24. copyright©amberpasillas2010 Multiplying Powers: If bases are the same add exponents. Power of a Power: Used when exponents are on the outside of parenthesis, just multiply exponents. Coefficients: The number in front of the variable is the coefficient. Multiply coefficients. #

25. copyright©amberpasillas2010 Dividing Powers: If bases are the same subtract exponents. Negative Exponent: To get rid of a negative exponent flip it over! Zero Exponent: Anything to the zero power is always one ! #