Simplify the expression: 2^{2/3} cdot 2^{1/5}.

Using the laws of exponents $a^m \cdot a^n = a^{m+n}$, we add the powers: $2/3 + 1/5$. The LCM of 3 and 5 is 15. So, $2/3 = 10/15$ and $1/5 = 3/15$. Adding them gives $13/15$. Thus, the simplified expression is $2^{13/15}$.