Convert fraction exponents to roots and exponents

[evykassirer]

this is only if the exponent is an integer fraction

e.g. 125 ^ 4/5 => (nthRoot(125, 5))^4

I have no strong opinions about its priority/grouping amongst the other simplifications. Maybe in its own DFS before function evaluation?

[evykassirer]

interestingly - cymath actually does something different: https://www.cymath.com/answer.php?q=125%20%5E%20(4%2F5)

I think pedagogically, it makes sense to convert to a root? Interested in pedagogy opinions on this though

[hmaurer]

I am not sure. Personally I always convert roots to fractional exponents where I can; I find them easier to reason about (you can use the standard exponent rules) and easier to draw. In this specific example I think cymath's approach is clearer.

[evykassirer]

hmm interesting - I can see pros/cons either way

I'll ask Socratic's content people about it next week and get their opinion on this :) (they've both done a lot of teaching)

[hmaurer]

If you are just learning arithmetic I guess nth-root might be less scary. Fractional exponents are a bit abstract, and mentally you usually think "ok x^3/4 is x^3 then take the 4th root". This might be one of those cases where it really depends on the context / student's preference, but I can see stronger arguments in favour of nth-roots for young students. Looking forward to hearing their opinion!

[kevinbarabash]

In the case of simplifying something like (nthroot(x, 5))^3 * (nthroot(x, 5))^4, it might be preferable to convert the roots to fractional exponents before simplifying, e.g.

x^(3/5) * x^(4/5) => x^(3/5 + 4/5) => x^((3+4)/5) => x^(7/5) => (nthroot(x, 5))^3

Another aspect of this is when render fractional exponents as roots, the exponent can be either on the inside our the outside:

(nthroot(x^3, 5)) <=> (nthroot(x, 5))^3