$\frac{1}{\frac{1}{9}+\frac{1}{27}+\frac{1}{18}}$
Thus, the solution to the given expression is \(\boxed{4.909090909090909}\).
Step 1 :Given the expression \(\frac{1}{\frac{1}{9}+\frac{1}{27}+\frac{1}{18}}\), we are asked to find the reciprocal of the sum of three fractions.
Step 2 :First, we calculate the sum of the three fractions: \(\frac{1}{9}+\frac{1}{27}+\frac{1}{18} = 0.2037037037037037\).
Step 3 :Next, we take the reciprocal of this sum: \(\frac{1}{0.2037037037037037} = 4.909090909090909\).
Step 4 :Thus, the solution to the given expression is \(\boxed{4.909090909090909}\).