Find the value of the expression: \( e^{2\cos^{-1}(\frac{1}{2})} \)

Step 1 ：Step 1: We know that \( \cos^{-1}(\frac{1}{2}) = \frac{\pi}{3} \) from basic trigonometric values. So, we substitute this into the expression.

Step 2 ：Step 2: Now the expression becomes \( e^{2 \cdot \frac{\pi}{3}} \)

Step 3 ：Step 3: Simplify the exponent to get \( e^{\frac{2\pi}{3}} \)