#### Answer

$$2x$$

#### Work Step by Step

Dividing by a fraction is equivalent to multiplying by its inverse:
$$\frac{x^{3}}{8}\div \frac{x^{2}}{16}=\frac{x^{3}}{8}\times \frac{16}{x^{2}}=\bigg(\frac{x^{2}\times x}{8}\bigg)\times \bigg(\frac{8\times 2}{x^{2}}\bigg).$$
Cancel the common factors $x^{2}$ and $8$, and the result is
$$2x.$$