So, yes, you should FOIL the exponents.
I'm having a hard time understanding how to go about simplifying this expression.
Should I use FOIL? I can't seem to find any videos or tutorials online with similar problems.
I have come close with the answer but I still don't get why the answer is x^(3b^2) not x^(-3b^2)
If anyone can offer some advice that would be much appreciated.
well let's take a look
$\Large \dfrac{\left(x^{a+b}\right)^{a-b}}{\left(x^{a-2b}\right)^{a+2b}}=$
$\Large \dfrac {x^{(a+b)(a-b)}}{x^{(a-2b)(a+2b)}}=$
$\Large \dfrac{x^{a^2-b^2}}{x^{a^2-4b^2}}=$
$\Large \dfrac{x^{a^2}x^{-b^2}}{x^{a^2}x^{-4b^2}}=$
$\Large x^{3b^2}$
$\Large -b^2 - (-4b^2)=3b^2$