How can you write a^8/a^6 in different ways?

Well, the simplest way would be to divide them:

$${\frac{{{\mathtt{a}}}^{{\mathtt{8}}}}{{{\mathtt{a}}}^{{\mathtt{6}}}}}$$ would equal a^(8-6) which would equal a²

Another way would be to expand the expression:

$${\frac{\left({\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}\right)}{\left({\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{a}}\right)}}$$

And then simplify it to a*a