Simplifying the expression, we have:
[tex]\begin{gathered} y^{\frac{2}{5}}•y^{\frac{1}{10}}=y^{\frac{2}{5}+\frac{1}{10}}\text{ (Using the product rule of exponents)} \\ y^{\frac{4}{10}+\frac{1}{10}}\text{ (Transforming the first fraction to add as like fractions)} \\ y^{\frac{5}{10}}=y^{\frac{1}{2}}\text{ (Adding fractions and simplifying)} \\ \text{The answer is y}^{\frac{1}{2}} \end{gathered}[/tex]