Derivative of a negative fractional power

Using the power rule with $n = -\frac{2}{3}$, we get $f'(x) = -\frac{2}{3} x^{-2/3 - 1}$. Subtracting 1 from the exponent requires writing $1 = \frac{3}{3}$, so $-\frac{2}{3} - \frac{3}{3} = -\frac{5}{3}$.

Therefore $f'(x) = -\frac{2}{3} x^{-5/3}$. This can also be written as $f'(x) = -\dfrac{2}{3x^{5/3}}$, since a negative exponent indicates a reciprocal.