1. $x^{\frac{1}{3}} \cdot x^{\frac{2}{3}} \rightarrow x^{\frac{1}{3} + \frac{2}{3}} \rightarrow x^{1}$
2. $a^{\frac{1}{2}} \cdot a^{\frac{1}{4}} \rightarrow a^{\frac{1}{2} + \frac{1}{4}} \rightarrow a^{\frac{3}{4}}$
3. $\frac{m^{\frac{3}{5}}}{m^{\frac{1}{5}}} \rightarrow m^{\frac{3}{5} - \frac{1}{5}} \rightarrow m^{\frac{2}{5}}$
4. $(x^{-1} y^{-2})^{-\frac{1}{2}} \rightarrow x^{(-1)(-\frac{1}{2})} y^{(-2)(-\frac{1}{2})} \rightarrow \frac{1}{x^{\frac{1}{2}} y}$
5. $\left(\frac{y^{\frac{1}{3}}}{y^{\frac{1}{6}}}\right)^{2} \rightarrow (y^{\frac{1}{3} - \frac{1}{6}})^{2} \rightarrow (y^{\frac{1}{6}})^{2} \rightarrow y^{\frac{1}{3}}$
Parent Tip: Review the logic above to help your child master the concept of simplifying expressions with rational exponents worksheet.