How do we say km2 in words? Do we use km exponent by two, square kilometer, kilometer squared or something else?
Depends on the context.
If you are referring to an area then square kilometres is correct - but if it's a scientific unit that happens to be in length^2 then kilometres-squared.
edit: Checked the SI recommendations.
Although in general you would say kilomtres-squared when reading a formula, they recommend that if the length^2 represents an area eg. Pressure = N/m^2, then you read it as newtons-per-square-metre, since it is the area of a real square metre. I can't off-hand think of any units that are length^2 where it isn't an area.
However if the unit has a different quantity squared, such as Acceleration = m/s^2 then you read it as per-second-squared since a square second has no meaning on it's own.
Square kilometers (or kilometres).
The correct terms when written in a formal context are:
Remember these are different.
Three kilometres squared is three kilometres on one side and three kilometres on the other side which is 9 square kilometres.
Three square kilometres is three kilometres on one side and one kilometre on the other side.
In a formulaic context 3 kilometres squared is written
3Km x 3Km
And 3 square kilometres is written like this
with the two being an exponent (supertext).
'3 kilometres squared' means, for me, a square of side 3km, but to others it means 3 square kilometres. The official terminology is square kilometres, not kilometres squared, but since there is no agreement on its meaning better not use the expression 'kilometres squared', but, if it's what you mean, say square kilometres instead, or, as mentioned above 'key-emm squared'. If you mean a square of side 3km then say that, which I think is a pity.