Step 1 :The given expression is \(\frac{1}{21} *-17 *-21 * \frac{1}{17}\).
Step 2 :We can simplify this by cancelling out the common terms.
Step 3 :The terms 21 and -21 cancel each other out, as do the terms 17 and -17.
Step 4 :This leaves us with \(\frac{1}{1}\), which is simply 1.
Step 5 :So, the value of \(\frac{1}{21} *-17 *-21 * \frac{1}{17}\) is \(\boxed{1}\).