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Exponents and Monomials
Monomial is an expression that is anumber, a variable, or a product of anumber and variables.Constant is a monomial contai...
Laws of Exponents                                     1Negative Exponents:   a   −n                                   = n ...
Laws of Exponents                       m                      a              m −nDividing Powers:        n    =a         ...
Laws of Exponents                           n     n                       a     aPower of a Quotient:   = n           ...
Examples using the laws of exponents:1. (2ab        )(−3a b c ) = −6a b c           2        4 2        5 42. (6x y2 3    ...
−10x y 2   44.      4 = −2x    5xy5. (x    )= x        2 4                  86. (−2a b      ) = 16a          3   2 4      ...
2    3x y        3 n7.  5 3n 2    x y z              2   3           9=  2 2n 2  = 4 4n 4  x y z     x y z
−3        3        3    4   n   n8.   =      =          4  64     n            −3                −3     3x y   ...
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  1. 1. Exponents and Monomials
  2. 2. Monomial is an expression that is anumber, a variable, or a product of anumber and variables.Constant is a monomial containing novariables.Coefficient is a numerical factor of amonomial.Degree is the sum of the exponents of amonomial’s variables.Power is the expression of the form xn.
  3. 3. Laws of Exponents 1Negative Exponents: a −n = n a 1 a −n =a n m +nMultiplying Powers: a g a = a m n
  4. 4. Laws of Exponents m a m −nDividing Powers: n =a aPower of a Power: (a ) =a m n mn ( ab ) mPower of a Product: =a b m m
  5. 5. Laws of Exponents n n a aPower of a Quotient:   = n  b b −n n b a   = bn aPower of Zero: a = 1 0
  6. 6. Examples using the laws of exponents:1. (2ab )(−3a b c ) = −6a b c 2 4 2 5 42. (6x y2 3 )(−xyz ) = −6x y z 3 4 12 x3. 4 = x 8 x
  7. 7. −10x y 2 44. 4 = −2x 5xy5. (x )= x 2 4 86. (−2a b ) = 16a 3 2 4 12 8 b
  8. 8. 2  3x y  3 n7.  5 3n 2  x y z  2  3  9=  2 2n 2  = 4 4n 4 x y z  x y z
  9. 9. −3 3 3  4  n n8.   = =  4  64 n −3 −3  3x y   x  3b 2b9.  b 3 =  2  −6x y   −2y  2 3  −2y  −8y 6 =  2b  = 6b  x  x
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