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7.4 MULTIPLICATION AND EXPONENTS:

Base: A number that is multiplied repeatedly. 7.4 MULTIPLICATION 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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7.4 MULTIPLICATION AND EXPONENTS:

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  1. Base: A number that is multiplied repeatedly. 7.4 MULTIPLICATION 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. 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

  5. YOU TRY IT: • Simplify: • (124)-2 • ((-2)5)-2 • (m3 )-1 ∙ m5 • (9-3 )2∙ 9-4

  6. SOLUTION: No matter what integer it is, anything to the power of zero is 1. (124)-2   12(4)(-2)  12-8 2) ((-2)5)-2   (-2)(5)(-2)  (-2)-10 3) (m3)-1 ∙ m5  m(3)(-1)+5  m-3+5  m2 4) (9-3)2∙ 9-4   9(-3)(2)-4  9-10

  7. 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

  8. YOU TRY IT: • Simplify: • (12y)-2 • (-2c)5 • (mz)3∙ m5 • (9-3 n)2∙ 9-4

  9. SOLUTION: No matter what integer it is, anything to the power of zero is 1. (12y)-2    12-2y-2 2) (-2c)5  (-2)5c5  -32c5 3) (mz)3 ∙ m5  m3z3m5  m3+5z3  m8z3 4)(9-3z)2∙ 9-4   9(-3)(2)z2 ∙ 9-4  9-10 z2

  10. 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

  11. EXAMPLE: Simplify: (5×104)3(6×10-2) (3×10-5) 3(4×10-2) (1.13×10-7)3(9.8×105 )(3.34×1022)

  12. SOLUTION: 1) (5×104)3(6×10-2 ) = 7.50×1012 (53)(6)× 10(4)(3)-2 750× 1010 2) (3×10-5)3(4×10-2 ) (33)(4)× 10(-5)(3)-2 108× 10-17 1.08×10-15 3) (1.13×10-7)3(9.8×105 )(3.34×1022) (1.133)(9.8)(3.34)× 10(-7)(3)+5+22 47.23× 106 4.723× 107

  13. 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

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

  15. 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 = =

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

  17. VIDEO: Raising a Power to a Power With Exponents http://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/exponent-properties-3

  18. CLASSWORK:Page 436-437: Problems: As many as needed to master the concept

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