---
title: "Ivory: By Your Powers Combined"
---

> | Try, if you can to come where we have gone
> | You may achieve what can't be simply done
> | Look back and there you are where we have been
> | And still there's so much in between
— <cite>Helloween, *Power*</cite>

TODO

 - Exponents let us implement reciprocals (powers of 1̅), and hence fractions
 - Exponents interact with each other and with products, but not sums
   - This page should focus on their normalisation rules, as an extension to the
     sums-and-products page
   - Normal form is likely to be the fixed point of
     'x = sums-of-products-of-exponents-of x'
 - Fractional exponents give us radicals; save that for the radical page

Maybe better off as a function, rather than a representation. I think we only
need one level of fraction, with a polynomial (sum of products) on top and on
bottom. Radical numbers can be made by "indexing" a √ symbol.