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7.5 DIVISION AND EXPONENTS:

Base: A number that is multiplied repeatedly. 7.5 DIVISION AND EXPONENTS:. Exponent: A number that shows repeated multiplication. Property: A character or attribute that something has. GOAL:. Remember:. An exponent equation has two components:. Exponent. Base.

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7.5 DIVISION AND EXPONENTS:

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  1. Base: A number that is multiplied repeatedly. 7.5 DIVISION AND EXPONENTS: 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: Exponent Base

  4. Dividing with Exponents PROPERTIES: For every number a≠0 and m, n, are integers, = Ex: 1) = 35-3 = 9 = 32 2) = =

  5. Simplify: 1) 2) 3) 4) YOU TRY IT:

  6. SOLUTION: Always move the smaller exponent to the opposite side. 1)   2)    3)  4)  

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

  8. YOU TRY IT: Simplify: 1) 3)

  9. SOLUTION: With parenthesis, the exponent distributes to the numerator and denominator: 1)         3) 

  10. Dividing with Exponents PROPERTIES: For every number a≠0 and m, n, are integers, = Ex: 1) = x 105-3 = 1.5x 102 2) =x 10-8+1 =8.8x 10-8

  11. YOU TRY IT: Simplify: 1) 2) 3)

  12. SOLUTION: With scientific notation, we divide the numbers and subtract/add the exponents of the base 10. 1)   4 2)   0.4  4 3)   0.7  7

  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. ZERO: as an exponent PROPERTIES: For every number a, = 1 Ex: (-3)0= 1 40= 1 1000= 1 -½ 0= -1 1,000,0000= 1

  16. Negative numbers: as an exponents PROPERTIES: For every nonzero number a≠0, and integer n = Ex: 2) (-3)-2= 1) 4-1=

  17. Multiplying powers withsame base: PROPERTIES: For every number a≠0 and m, n, are integers, = Ex: 1) 41∙ 43= 41+3= 44= 256 2) 31∙ 3-3= 31+-3= 3-2 = =

  18. Raising powers to powers: PROPERTIES: For every number a≠0 and m, n, are integers, = Ex: = 41∙3 1) (41)3 = 43 = 64 = = = 3-3 = 31 ∙ -3 2) (31)-3

  19. Raising a product to powers: PROPERTIES: For every number a≠0 and m, n, are integers, = Ex: 1) (4x)3 = 43x3 = 64x3 = = 2) (3s)-3 = 3-3s-3

  20. Dividing with Exponents PROPERTIES: For every number a≠0 and m, n, are integers, = Ex: 1) = 35-3 = 9 = 32 2) = =

  21. Dividing with Exponents PROPERTIES: For every number a≠0, b ≠0 and man integers, = Ex: = = 2) = =

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

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

  24. Dividing with Exponents PROPERTIES: For every number a≠0 and m, n, are integers, = Ex: 1) = x 105-3 = 1.5x 102 2) =x 10-8+1 =8.8x 10-8

  25. VIDEOS: Exponents andDivision https://www.khanacademy.org/math/arithmetic/exponents-radicals/exponent-properties/v/exponent-properties-involving-quotients

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

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