Question 151353

{{{(-16x^7y^5 )/(-4x^2y^6)}}} Start with the given expression.



{{{(-2*2*2*2*x*x*x*x*x*x*x*y*y*y*y*y)/(-2*2*x*x*y*y*y*y*y*y)}}} Expand. Remember, {{{-16x^7y^5 =-2*2*2*2*x*x*x*x*x*x*x*y*y*y*y*y}}} and {{{-4x^2y^6=-2*2*x*x*y*y*y*y*y*y}}}



{{{(highlight(-2)*highlight(2)*2*2*highlight(x)*highlight(x)*x*x*x*x*x*highlight(y)*highlight(y)*highlight(y)*highlight(y)*highlight(y))/(highlight(-2)*highlight(2)*highlight(x)*highlight(x)*highlight(y)*highlight(y)*highlight(y)*highlight(y)*highlight(y)*y)}}} Highlight the common terms.



{{{(cross(-2)*cross(2)*2*2*cross(x)*cross(x)*x*x*x*x*x*cross(y)*cross(y)*cross(y)*cross(y)*cross(y))/(cross(-2)*cross(2)*cross(x)*cross(x)*cross(y)*cross(y)*cross(y)*cross(y)*cross(y)*y)}}} Cancel out the common terms.



{{{(2*2*x*x*x*x*x)/(y)}}} Simplify.



{{{(4*x^5)/(y)}}} Regroup.



So {{{(-16x^7y^5 )/(-4x^2y^6)}}} simplifies to {{{(4*x^5)/(y)}}}.



In other words, {{{(-16x^7y^5 )/(-4x^2y^6)=(4*x^5)/(y)}}} where  {{{x<>0}}} or {{{y<>0}}}