Question 187161
{{{(24x^3y^5)/(40x^7y^2)}}} Start with the given expression.



{{{(2*2*2*3*x*x*x*y*y*y*y*y)/(2*2*2*5*x*x*x*x*x*x*x*y*y)}}} Expand. Note: {{{24x^3y^5=2*2*2*3*x*x*x*y*y*y*y*y}}} (there are 3 x's and 5 y's) and {{{40x^7y^2=2*2*2*5*x*x*x*x*x*x*x*y*y}}} (there are 7 x's and 2 y's)



{{{(highlight(2)*highlight(2)*highlight(2)*3*highlight(x)*highlight(x)*highlight(x)*highlight(y)*highlight(y)*y*y*y)/(highlight(2)*highlight(2)*highlight(2)*5*highlight(x)*highlight(x)*highlight(x)*x*x*x*x*highlight(y)*highlight(y))}}} Highlight the common terms.



{{{(cross(2)*cross(2)*cross(2)*3*cross(x)*cross(x)*cross(x)*cross(y)*cross(y)*y*y*y)/(cross(2)*cross(2)*cross(2)*5*cross(x)*cross(x)*cross(x)*x*x*x*x*cross(y)*cross(y))}}} Cancel out the common terms.



{{{(3*y*y*y)/(5*x*x*x*x)}}} Simplify.



{{{(3*y^3)/(5*x^4)}}} Regroup and multiply.



So {{{(24x^3y^5)/(40x^7y^2)}}} simplifies to {{{(3*y^3)/(5*x^4)}}}.



In other words, {{{(24x^3y^5)/(40x^7y^2)=(3*y^3)/(5*x^4)}}} where {{{x<>0}}} or {{{y<>0}}}




Note: this is the long way to solve this type of problem, but it helps you visualize what's going on.