If I have let's say
If I take the reciprocal of the left hand side to eliminate the minus, do I have to do the same for both sides of the equation?
But why would you like to get the reciprocal of x^(-1/3) to make the -1/3 power become 1/3 power?
The reciprocal of x^(-1/3) is 1 / x ^(-1/3) = x^(1/3)
So you new equation is x^(1/3) = 1/(2x).
Why not just put the x^(-1/3) at the denominator to "eliminate the negative"?
= 1 / x^(1/3)
1 / x^(1/3) = 2x.
Of course, whichever way,
2x * x^(1/3) = 1