7x^(1/3)-x(-2/3)=0

7x^(1/3)-x(-2/3)=0    factor

x^(-2/3) (7x- 1) = 0

The first factor is never 0

For the second one, we have

7x - 1  = 0

Add 1 to both sides

7x = 1    divide both sides by 7

x = 1/ 7 = about .1428

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Use the calculator on the homepage....

Let y = x^1/3, then your equation becomes 

7y - 1/y² = 0  (I've assumed your equation is meant to be 7x^1/3 - x^-2/3 = 0)

Multiply through by y²

7y³ - 1 = 0

so

y³ = 1/7

But y³ = x so x = 1/7

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