If knowledge is power...

Wisdom is an elaborated knowledge. It is more based on the own experience than knowledge itself is. So wisdom requires a higher age. Wise people are old. If younger people seem to be wise, to have wisdom, then they are “altklug” (“old-clever”), precocious (is that the correct English word for it?).

B.t.w.: Knowledge is not always power, because it depends on the magnitude and distribution of power in each and every situation. There are (for example) poor people who are wise, but they have no power, in any case no societal power.