>Hi Bruce,
>
>>you just built your own recursive multiplier for integers, but for fractional powers, it wasn't so easy...
>
>How would you do it (fractions I mean)? I've got some ideas (using easy ones as templates). But they don't teach us that in HS, just how to hit it on a calculator, and I've taken every math class in the school.

The Taylor Series is a standard way, where ' means derivative:

to estimate some function like x^1.5, f(x) = f(a) + f'(a)*(x-a) - f''(a)*(x-a)^2/2! + f'''(a)*(x-a)^3/3! - ...where a is some arbitrary point, often taken to be 1 for obvious convenience :)

Kind of messy, but gets accurate pretty fast, so you don't need to find too many orders of derivatives. There's an "error function" also, so you can predict how much accuracy you'll get...there are other ways too, if you take a year of Numerical Analysis, you'll be sure to see some of them < s > In casy you need the 7th root of 45 and you're trapped on a desert island with no computer...