To simplify \( 4^{-1/2} \), we start by rewriting it using the properties of exponents:
\[ 4^{-1/2} = \frac{1}{4^{1/2}} \]
Next, we know that \( 4^{1/2} \) is the square root of 4:
\[ 4^{1/2} = \sqrt{4} = 2 \]
Now, substituting this back into our expression:
\[ 4^{-1/2} = \frac{1}{2} \]
Thus, the simplified form of \( 4^{-1/2} \) is:
\[ \frac{1}{2} \]