18. \( x^{\frac{1}{2}} \cdot x^{-\frac{2}{3}} \)

To simplify \( x^{\frac{1}{2}} \cdot x^{-\frac{2}{3}} \), you can use the property of exponents which states that when multiplying like bases, you add the exponents. So, we have: \[ x^{\frac{1}{2} - \frac{2}{3}} \] To combine the fractions, find a common denominator, which is 6: \[ \frac{1}{2} = \frac{3}{6} \quad \text{and} \quad -\frac{2}{3} = -\frac{4}{6} \] Now, adding these gives: \[ \frac{3}{6} - \frac{4}{6} = -\frac{1}{6} \] Thus, the expression simplifies to: \[ x^{-\frac{1}{6}} \] And if needed, this can be expressed as: \[ \frac{1}{x^{\frac{1}{6}}} \]