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

A negative exponent means a reciprocal: $x^{-3/2} = \frac{1}{x^{3/2}}$. A fractional exponent $\frac{3}{2}$ means the square root of the cube: $x^{3/2} = \sqrt{x^3}$. Combining them gives $\frac{1}{\sqrt{x^3}}$, choice C. Choice A ($-x^{3/2}$) treats the negative exponent as a negative sign, which is wrong. Choice B ($\sqrt{x^3}$) is $x^{3/2}$ itself, with the reciprocal forgotten. Choice D ($\frac{1}{x^3}$) ignores the square root, which would be $x^{-3}$. The denominator 2 of the exponent signals a square root.