The easiest way to do this is to split that numerator up into each of its individual expressions over the denominator, like this: [tex] \frac{-5w^{10}}{5w^5}+ \frac{10w^8}{5w^5}+ \frac{5w^6}{5w^5} [/tex] and then divide each expression one at a time. In the first expression, -5 diivided by 5 = -1. Now for the exponents. As long as the base is the same you will subtract the exponents, lower from upper. Our bases are all w's, so we're good. [tex]w^{10-5}=w^5[/tex] so that expression is [tex]-w^5[/tex]. Now for the second expression. 10 divided by 5 is 2, and, using our rules for dividing exponents with like bases, [tex]w^{8-5}=w^3[/tex]. So that expression is [tex]2w^3[/tex]. For the last term there, 5 divided by 5 is 1, and [tex]w^{6-5}=w^1=w[/tex]. Now we will put all of them together to get a final solution of [tex]-w^5+2w^3+w[/tex]. There you go!