This is the 12157th most frequent Russian word.
императору
Dative case of "император" (emperor) – "to the emperor" or "for the emperor."
The word 'императору' is in the dative case, indicating the recipient of the action, which is typical for the verb 'преподнести' (to present).
Мы подношение преподнесли императору.
We presented an offering to the emperor.
Here, 'императору' is also in the dative case, used with the verb 'улыбнуться' (to smile), describing the direction of the action.
Она по-особенному улыбнулась императору.
She smiled especially at the emperor.
In this example, 'императору' once again uses the dative case to show the recipient of dedication, as indicated by 'посвятить' (to dedicate).