Step 1 :The problem is asking for the square root of \(w^{18}\). The square root of a number is the value that, when multiplied by itself, gives the original number. In this case, we need to find the value that, when squared, gives \(w^{18}\).
Step 2 :We know that the square root of \(w^{18}\) can be written as \((w^{18})^{1/2}\).
Step 3 :Using the rule of exponents, we can simplify this to \(w^{18/2}\), which is \(w^9\).
Step 4 :Final Answer: \(\boxed{w^9}\)