Evaluate the exponential expression [math](3^{\frac{1}{2}})^{\frac{4}{3}}[/math]. Round your answer to the nearest thousandth.
[list=1] [*]Simplify the expression using properties of exponents. [*]Write the rational exponent in simplest form. Be sure to include absolute value if the original expression involved finding an even root. [*]Evaluate the power and root of the function, using a calculator if needed. [/list]