# Why is 'something per hectare' denoted with a negative exponent ( $ha^{-1}$)?

Quick question.... why is it that something per hectare is shown as having a negative exponent, $ha^{-1}$?

1 tonne per hectare is shown as (t $ha^{-1}$).

I did some searching and can't find a good explanation. Any ideas?

This is because something to the power of $-1$ is equivalent the following;

to $$\frac{1}{t}=t^{-1}$$

and for example

$$\frac{1}{t^3}=t^{-3}$$

So it should make more sense now as it is $$\frac{something}{hectare}$$ in your example , or as I said above, $$something(hectare)^{-1}$$

• Thank you for the explanation, that makes perfect sense. Cheers. – AggroCrag May 14 '15 at 4:44
• No problem, glad it helped – Quality May 14 '15 at 4:45

Per hectare means = rate of 1 hectare.

per means the value should go in denominator and nominator with 1 is 1/ha = ha^-1

It's an algebra thing. We denote $\frac{1}{a}$ as $a^{-1}$. So $\frac{1}{ha}=ha^{-1}$.

Suppose I'm selling you land at a cost of \$100 per hectare. If I sell you 20 hectares, the cost should be "20 hectares" times "\$100 per hectare", and that needs to work out to "\$2000". The only way these units can work out is if "\$100 per hectare" means "100 dollars * ha^-1", so that the hectares and inverse-hectares cancel in the multiplication.