Evaluate the left hand side to find the value of \( a \) in the equation is simplest form. \[ \left(x^{\frac{1}{2}}\right)^{\frac{6}{5}}=x^{a} \]

To evaluate the left-hand side \( \left(x^{\frac{1}{2}}\right)^{\frac{6}{5}} \), we can use the power of a power property of exponents, which states that \( (x^m)^n = x^{m \cdot n} \). Applying this property, we multiply the exponents: \[ \left(x^{\frac{1}{2}}\right)^{\frac{6}{5}} = x^{\frac{1}{2} \cdot \frac{6}{5}} = x^{\frac{6}{10}} = x^{\frac{3}{5}}. \] So, we can equate it to the right-hand side \( x^{a} \), giving us \( a = \frac{3}{5} \). Thus, the value of \( a \) is \( \frac{3}{5} \).