Question

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

Answer 1

The easiest way to do this is to split that numerator up into each of its individual expressions over the denominator, like this:  $\frac{-5w^{10}}{5w^5}+ \frac{10w^8}{5w^5}+ \frac{5w^6}{5w^5}$  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.  $w^{10-5}=w^5$  so that expression is  $-w^5$.  Now for the second expression.  10 divided by 5 is 2, and, using our rules for dividing exponents with like bases,  $w^{8-5}=w^3$.  So that expression is  $2w^3$.  For the last term there, 5 divided by 5 is 1, and  $w^{6-5}=w^1=w$.  Now we will put all of them together to get a final solution of  $-w^5+2w^3+w$.  There you go!