Which expression is equivalent to x³/2 for x > 0?

A fractional exponent means a root and a power: $x^{m/n} = \sqrt[n]{x^m}$. Here $x^{3/2} = \sqrt{x^3}$, choice C. It can also be written $(\sqrt{x})^3$. Choice A, $3x^{1/2}$, multiplies by 3 rather than raising to the third power. Choice B, $\frac{x^3}{x^2}$, simplifies to $x$, which is not $x^{3/2}$; subtracting exponents gives $3 - 2 = 1$. Choice D, $2x^3$, treats the denominator 2 as a coefficient and the numerator as the entire exponent, which is also incorrect. The denominator of the exponent is the root index.