Question

When foiling out something like this:

(8x^3/4 - 8y^1/2) (5x^3/4 - 3y(1/2)

How do you do it?
I can't figure out what to do with the fractional exponents.

Answer 1

There is a property from algebra that says that (a*x^n) * (b*x^m) = (a*b)*x^(n+m). It works if n or m are any number, I think.

When you get to the ones that are like (a*x^n) * (b*y^m), then the most you can do is say that it is equal to (a*b) * x^n * y^m. I mean, x and y have to be the same to apply the property above.

You might not be able to simplify that expression you have above, beyond applying the property I just mentioned.

Answer 2

(where this property comes from, is that x^n = (x*x*...*x) n times. And x^m = (x*x*...*x) m times. Then x^n * x^m = (x*x*...*x) * (x*x*...*x) where in the first bracket there are n x's multiplied together, and in the second there are m x's multiplied together, so if you take away the brackets, there are n + m x's all up, multiplied together. So it's equal to x^(n+m). To extend it so that n and m can be rational numbers, uses pretty much the same idea as above.)