divide (-5w^10+10w^8+5w^6)/(5w^5)

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!