# Converting Units with Exponents

Reference > Science > Unit ConversionsWe've now covered almost everything you need to know in order to be an expert unit-converter. But there's one more scenario we should talk about: what happens if your units have exponents?

"What? Units can have exponents?"

Sure! Units of area are things like ft^{2} and in^{2}. Volume uses cubes (meter^{3}), and when you deal with physics, you'll get some really scary units like kilogram x meter/second^{2}!

Don't panic, though; it's really not all that difficult...**Example One** - Convert 12 ft^{2} to inches^{2}.

We start off as we normally do, by multiplying by our conversion factor (12 inches)/(1 foot):

(12 ft^{2}) x (12 inches)/(1 foot) = 144 foot x inches.

You see what happened? *One* of the feet in feet^{2}canceled, leaving us with a unit of *foot x inch*.

WHAT? That's a ridiculous looking unit - who ever heard of a foot-inch? What went wrong? Nothing went wrong. We just need to multiply our conversion factor TWICE:

(144 foot x inches) x (12 inches)/(1 foot) = 1728 inches^{2}*If a unit has an exponent of 2, you need to daisy chain the conversion factor twice to get rid of the unit!*

In fact, we can generalize that:

*If a unit has an exponent of*

**n**, we need to daisy chain the conversion factor**n**times to get rid of the unit.**Example Two** - Convert 81 feet^{3} to yards^{3}**Answer** - Our conversion factor is (1 yard)/(3 feet), and we need to daisy chain it 3 times. But daisy chaining the conversion factor 3 times is the same as cubing it, right? So let's cube that conversion factor:

(1^{3} yard^{3})/(3^{3} feet^{3}) = (1 yard^{3})/(27 feet^{3}).

Now let's use that conversion factor:

(81 feet^{3}) x (1 yard^{3})/(27 feet^{3}) = 3 yard^{3}.

## Questions

^{2}to hours

^{2}.

^{2}to miles/min

^{2}