Find the exact value of the following expression, if possible. \[ \sin ^{-1}\left(\sin \frac{\pi}{10}\right) \]

Step 1 ：The given expression is \(\sin ^{-1}\left(\sin \frac{\pi}{10}\right)\).

Step 2 ：The inverse sine function, or arcsin, is the inverse function of sine, which means it undoes the operation of sine.

Step 3 ：So, if we have \(\sin^{-1}(\sin(x))\), the sine and inverse sine will cancel each other out, leaving us with \(x\).

Step 4 ：However, this is only true if \(x\) is in the domain of \(\sin^{-1}\), which is \([-\frac{\pi}{2}, \frac{\pi}{2}]\).

Step 5 ：Since \(\frac{\pi}{10}\) is in this domain, we can directly apply this property.

Step 6 ：Thus, the exact value of the expression \(\sin ^{-1}\left(\sin \frac{\pi}{10}\right)\) is \(\frac{\pi}{10}\).

Step 7 ：\(\boxed{\frac{\pi}{10}}\) is the final answer.