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

— Helloween, Power

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.