Step 1 :Given the function \(f(x, y)=2^{x}+9 x y\), we are asked to find the values of \(f(0,-3)\), \(f(-3,2)\), and \(f(3,2)\).
Step 2 :To find these values, we substitute the given x and y values into the function and simplify.
Step 3 :For \(f(0,-3)\), we substitute \(x=0\) and \(y=-3\) into the function to get \(2^{0}+9*0*(-3)\), which simplifies to 1.
Step 4 :For \(f(-3,2)\), we substitute \(x=-3\) and \(y=2\) into the function to get \(2^{-3}+9*(-3)*2\), which simplifies to -53.875.
Step 5 :For \(f(3,2)\), we substitute \(x=3\) and \(y=2\) into the function to get \(2^{3}+9*3*2\), which simplifies to 62.
Step 6 :So, the final answers are \(f(0,-3)=\boxed{1}\), \(f(-3,2)=\boxed{-53.875}\), and \(f(3,2)=\boxed{62}\).