Which expression is equivalent to x^-2/3 for x > 0?

A negative exponent indicates a reciprocal: $x^{-2/3} = \frac{1}{x^{2/3}}$. A fractional exponent $\frac{m}{n}$ means the $n$th root of the $m$th power, so $x^{2/3} = \sqrt[3]{x^2}$. Combining these, $x^{-2/3} = \frac{1}{\sqrt[3]{x^2}}$, choice A. Choice B ($-x^{2/3}$) treats the negative exponent as a negative sign in front, which is wrong. Choice C ($\sqrt[3]{x^2}$) drops the reciprocal, equal to $x^{2/3}$. Choice D ($\frac{-1}{x^{2/3}}$) has the reciprocal but adds an extra negative sign. A negative exponent never makes the value negative for positive $x$.