We'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 ft² and in². Volume uses cubes (meter³), and when you deal with physics, you'll get some really scary units like kilogram x meter/second²!

Don't panic, though; it's really not all that difficult...

Example One - Convert 12 ft² to inches².

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

(12 ft²) x (12 inches)/(1 foot) = 144 foot x inches.

You see what happened? One of the feet in feet²canceled, 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 inches²

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 feet³ to yards³

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: 

(1³ yard³)/(3³ feet³) = (1 yard³)/(27 feet³).

Now let's use that conversion factor:

(81 feet³) x (1 yard³)/(27 feet³) = 3 yard³.