Question 195727

{{{(48x^3y^2)/(8x^7y^2)}}} Start with the given expression.



{{{(2*2*2*2*3*x*x*x*y*y)/(2*2*2*x*x*x*x*x*x*x*y*y)}}} Expand. 



Note: {{{48x^3y^2=2*2*2*2*3*x*x*x*y*y}}} and {{{8x^7y^2=2*2*2*x*x*x*x*x*x*x*y*y}}}



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



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



{{{(2*3)/(x*x*x*x)}}} Simplify.



{{{6/(x^4)}}} Multiply.



So {{{(48x^3y^2)/(8x^7y^2)}}} simplifies to {{{6/(x^4)}}}.



In other words, {{{(48x^3y^2)/(8x^7y^2)=6/(x^4)}}} where every variable is non zero