Question

Fie numerele
a=(-3/4)*(-3/4)^2*(-3/4)^3*...(-3/4)^2014*(-3/4)^2015 si
b=(-4/3)*(-4/3)^2*(-4/3)^3*...(-4/3)^2015*(-4/3)^2016

Calculati valoarea lui n=a*b:(-64/27)^336

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Answer 1

a=(-3/4)*(-3/4)^2*(-3/4)^3*...(-3/4)^2014*(-3/4)^2015  = 
    (-3/4)^(2015x2016:2) =
    (-3/4)^(2015 x 1008) =
     (- 3/4)^ 2031120 = 
      (3/4)^ 2031120

b=(-4/3)*(-4/3)^2*(-4/3)^3*...(-4/3)^2015*(-4/3)^2016  = 
   ( -4/3)^ (2016x2017:2)= 
   ( - 4/3)^(1008 x2017) = 
   (- 4/3)^2033136 
    (4/3)^2033136 

n=a*b:(-64/27)^336 = 
   (3/4)^2031120 x (4/3)^2033136 : [(4/3)^3]^336 = 
   (3/4)^2031120 x (4/3)^2033136 : (4/3)^1008= 
    (3/4)^2031120 x (4/3)^2033136 x (3/4)^1008 = 
    (4/3)^ 2033136 x (3/4)^2032128 = 
     4^1008 /3^-1008 = 
     (4 x 3)^1008 =
      12^1008