3) \( \frac{3 u^{-\frac{1}{3}} v^{\frac{1}{2}}}{3 u^{-1} v^{-2}} \)

To simplify the expression \( \frac{3 u^{-\frac{1}{3}} v^{\frac{1}{2}}}{3 u^{-1} v^{-2}} \), we first cancel out the common factor of 3: \[ \frac{u^{-\frac{1}{3}} v^{\frac{1}{2}}}{u^{-1} v^{-2}} \] Now we can apply the laws of exponents: 1. For \(u\): \[ u^{-\frac{1}{3}} \div u^{-1} = u^{-\frac{1}{3} - (-1)} = u^{-\frac{1}{3} + 1} = u^{\frac{2}{3}} \] 2. For \(v\): \[ v^{\frac{1}{2}} \div v^{-2} = v^{\frac{1}{2} - (-2)} = v^{\frac{1}{2} + 2} = v^{\frac{1}{2} + \frac{4}{2}} = v^{\frac{5}{2}} \] Combining these results, the simplified expression is: \[ u^{\frac{2}{3}} v^{\frac{5}{2}} \] So the final answer is: \[ u^{\frac{2}{3}} v^{\frac{5}{2}} \]