Fractional Exponents: ACT Math Practice Question

Try the following ACT math practice question that tests your understanding of manipulating fractional exponential expressions.

If $x$ is a positive number, which of the following is equivalent to $x^{\frac{5}{2}}$ ?

1. $x^2 \sqrt{x}$
2. $x (\sqrt{x})^3$
3. $\displaystyle \frac{x^3}{\sqrt{x}}$

1. $\quad \textrm{I and II only}$
2. $\quad \textrm{I and III only}$
3. $\quad \textrm{II and III only}$
4. $\quad \textrm{I, II, and III}$
5. $\quad \textrm{None}$

Choice D