1. 7.5 DIVISION AND EXPONENTS: Base: A number that is multiplied repeatedly. Exponent: A number that shows repeated multiplication. Property: A character or attribute that something has.

2. GOAL:

3. Remember: An exponent equation has two components: Base Exponent

4. PROPERTIES: Dividing with Exponents For every number a≠0 and m, n, are integers, Ex: = 3 5-3 = 3 2 = 9

5. YOU TRY IT:

6. SOLUTION: Always move the smaller exponent to the opposite side.

7. PROPERTIES: Dividing with Exponents For every number a≠0, b ≠0 and m an integers, Ex:

8. YOU TRY IT: Simplify:

9. SOLUTION: With parenthesis, the exponent distributes to the numerator and denominator:

10. PROPERTIES: Dividing with Exponents For every number a≠0 and m, n, are integers, Ex: = 1.5x 10 2 =8.8x 10 -8

11. YOU TRY IT:

12. SOLUTION: With scientific notation, we divide the numbers and subtract/add the exponents of the base 10.

13. VIDEO: Dividing With Exponents Dividing Powers http://www.khanacademy.org/math/algebra/exponent- equations/exponent-properties-algebra/v/exponent- properties-4

14. REMEMBER THE PROPERTIES:

15. PROPERTIES: ZERO: as an exponent For every number a, Ex: 4 0 = 1 (-3) 0 = 1 100 0 = 1 1,000,000 0 = 1 -½ 0 = -1

16. PROPERTIES: Negative numbers: as an exponents For every nonzero number a≠0, and integer n Ex:

17. PROPERTIES: Multiplying powers with same base: For every number a≠0 and m, n, are integers, Ex: 1) 4 1 ∙ 4 3 = 4 1+3 = 4 4 = 256

18. PROPERTIES: Raising powers to powers: For every number a≠0 and m, n, are integers, Ex: 1) (4 1 ) 3 2) (3 1 ) -3 = 4 1∙3 = 4 3 = 64 = 3 1 ∙ -3 = 3 -3

19. PROPERTIES: Raising a product to powers: For every number a≠0 and m, n, are integers, Ex: 1) (4x) 3 2) (3s) -3 = 4 3 x 3 = 64x 3 = 3 -3 s -3

20. PROPERTIES: Dividing with Exponents For every number a≠0 and m, n, are integers, Ex: = 3 5-3 = 3 2 = 9

21. PROPERTIES: Dividing with Exponents For every number a≠0, b ≠0 and m an integers, Ex:

22. PROPERTIES: Multiplying and Scientific notation For every nonzero number a, b and integer n and m (a×10 n )(b×10 m ) = a∙b×10 n+m

23. PROPERTIES: Multiplying and Scientific notation For every nonzero number a, b and integer n and m (a×10 n ) c (b×10 m ) = a c ∙b×10 (n)(c)+m

24. PROPERTIES: Dividing with Exponents For every number a≠0 and m, n, are integers, Ex: = 1.5x 10 2 =8.8x 10 -8

25. VIDEOS: Exponents and Division https://www.khanacademy.org/math/arithmetic/e xponents-radicals/exponent- properties/v/exponent-properties-involving- quotients

26. CLASSWORK: Page 443-445: Problems: As many as needed to master the concept