((8x/x^3-x^6/x^3))^-4/5

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Solution for ((8x/x^3-x^6/x^3))^-4/5 equation: 


D( x )

x^3 = 0

(8*x)/(x^3)-((x^6)/(x^3)) = 0

x^3 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

x = 0

(8*x)/(x^3)-((x^6)/(x^3)) = 0

(8*x)/(x^3)-((x^6)/(x^3)) = 0

(8*x)/(x^3)-x^3 = 0

8*x^-2-x^3 = 0

x^-2*(8-x^5) = 0

-1*x^5 = -8 // : -1

x^5 = 8

x^5 = 8 // ^ 1/5

x = 8^(1/5)

1/(x^2) = 0

1*x^-2 = 0 // : 1

x^-2 = 0

x należy do O

x in (-oo:0) U (0:8^(1/5)) U (8^(1/5):+oo)

(((8*x)/(x^3)-((x^6)/(x^3)))^-4)/5 = 0

(((8*x)/(x^3)-x^3)^-4)/5 = 0

1/(5*(8*x^-2-x^3)^4) = 0

8*x^-2-x^3 = 0

x^-2*(8-x^5) = 0

-1*x^5 = -8 // : -1

x^5 = 8

x^5 = 8 // ^ 1/5

x = 8^(1/5)

x^-2*(x-8^(1/5)) = 0

1/(5*(x^-2)^4*(x-8^(1/5))^4) = 0

x belongs to the empty set

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