"to the second/third/fourth power" would be "Hoch 2/3/4"

"Squared" is the more common form and would be equivalent to "quardiert" or "quadrat"

"cubed" would be a similar form of "hoch 3"

3 over the power of 2 equals 9

Soweit ich weiß ist das die Übersetzung

sorry, but "over" is not the word for "hoch" it is used to represent the german "durch" in the context of fractions

2/x would hence be "two over x"

x^2 (also x hoch 2)

x squared
x to the two
x to the second power
...

"over the power of 2" würde bei mir irritierte Blicke auslösen.



*edit*
Siehe auch im Wörterbuch
Dictionary: x hoch n