1. Properties of Exponents
Advanced Math Topics
Mrs. Mongold

2. Take a Piece of Paper and fold it in 4 to make a Frayer Organizer
Center on both sides is Exponent Properties

3. 1. Negative Exponents
For any real number a = 0 and any integer n, a-n =

4. 2. Product of Powers
For any real number a and integers m and n, am · an = am+n

5. 3. Quotient of Powers
For any real number a = 0, and any integers m and n, = am - n

6. 4. Power to a Power
Mulitply exponents when you have a power to a power , (am)n = amn

7. 5. Power of a Product
Distribute the exponent when you have a power of a product (ab)m = ambm

8. 6. Power of a Quotient
Take the numerator and denominator to the power outside,

9. 7. Zero Power
Any number raised to the 0 power is 1

10. 8. Fractional Exponents
A fractional exponent turns into a radical

11. Fractional Exponents

12. Fractional Exponents

13. Examples
42 ∙ 43

14. Examples
42 ∙ 43 =45 = 1024

15. Examples
42 ∙ 43 =45 = 1024
-3y ∙ -9y4

16. Examples
42 ∙ 43 =45 = 1024
-3y ∙ -9y4 = 27y5
(-4x3p2)(4y3x3)

17. Examples
42 ∙ 43 =45 = 1024
-3y ∙ -9y4 = 27y5
(-4x3p2)(4y3x3) = -16x6y3p2

18. Examples
42 ∙ 43 =45 = 1024
-3y ∙ -9y4 = 27y5
(-4x3p2)(4y3x3) = -16x6y3p2
-80

19. Examples
42 ∙ 43 =45 = 1024
-3y ∙ -9y4 = 27y5
(-4x3p2)(4y3x3) = -16x6y3p2
-80 = -1

20. (5x)0 + 5x0

21. (5x)0 + 5x0 = = 6

22. x9y6
x8y6

23. x9y6
x8y6 =x

24. -36a5b7c10
6ab3c4

25. -36a5b7c10
6ab3c4
= -6a4b7c6

26. 8r4
2r-4
y-7y y8
4x0 + 5

27. 8r4
2r-4
y-7y y8
4x0 + 5 = 9
=4r8

28. -3z4 ∙ 10z7
(4x)-1
30 – 3t0

30. x-7y-2
x2y2
(24x8)(x)
20x-7

31. x-7y-2
x2y2
(24x8)(x)
20x-7

32. Examples
Write each fractional exponent as a radical

33. Homework
Worksheet 1 & 2