((8x)^(2/3))*((9x^3)^(1/2))/((64x)^(1/2))^(1/3)

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Solution for ((8x)^(2/3))*((9x^3)^(1/2))/((64x)^(1/2))^(1/3) equation: 


D( x )

9*x^3 < 0

64*x < 0

((64*x)^(1/2))^(1/3) = 0

9*x^3 < 0

9*x^3 < 0

9*x^3 < 0

9*x^3 < 0 // : 9

x^3 < 0/9

x^3 < 0

x^3 < 0 // ^ 1/3

x < 0

x in (-oo:0)

64*x < 0

64*x < 0

64*x+0 < 0 // - 0

64*x < 0 // : 64

x < 0/64

x < 0

((64*x)^(1/2))^(1/3) = 0

((64*x)^(1/2))^(1/3) = 0

2*x^(1/6) = 0 // : 2

x^(1/6) = 0

x = 0

x in (0:+oo)

((8*x)^(2/3)*(9*x^3)^(1/2))/(((64*x)^(1/2))^(1/3)) = 0

6*x^2 = 0 // : 6

x^2 = 0

x = 0

x in { 0} 

x belongs to the empty set

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