To simplify the expression \((x^{\frac{2}{5}})^{10}\), we can use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\).
Applying this property:
\[ (x^{\frac{2}{5}})^{10} = x^{\frac{2}{5} \cdot 10} \]
Now, calculate the exponent:
\[ \frac{2}{5} \cdot 10 = \frac{2 \cdot 10}{5} = \frac{20}{5} = 4 \]
Thus, we have:
\[ (x^{\frac{2}{5}})^{10} = x^4 \]
So, the simplified expression is:
\[ \boxed{x^4} \]