Use properties of exponents to write the function in the form $f(t)=k a^{t}$, where $\mathrm{k}$ is a constant. \[ \left(\frac{1}{2}\right)^{1-2 t} \] \[ \left(\frac{1}{2}\right)^{1-2 t}= \]

Step 1 ：The given function is \(\left(\frac{1}{2}\right)^{1-2 t}\).

Step 2 ：We can rewrite it in the form \(f(t)=k a^{t}\) by using the properties of exponents.

Step 3 ：The properties of exponents state that \(a^{m-n} = \frac{a^m}{a^n}\).

Step 4 ：So, we can rewrite the given function as \(\frac{1}{2}^{1} \cdot \frac{1}{2}^{-2t}\).

Step 5 ：Then, we can simplify this to \(\frac{1}{2} \cdot 2^{2t}\).

Step 6 ：Finally, we can rewrite this as \(2^{2t-1}\).

Step 7 ：The function in the form \(f(t)=k a^{t}\) is \(f(t)=1 \cdot 2^{2t-1}\).

Step 8 ：\(\boxed{f(t)=2^{2t-1}}\) is the final answer.