Question 151296
{{{((u^3)/(w))/((uv^3)/(w^2))}}} Start with the given expression.




{{{((u^3)/(w))((w^2)/(uv^3))}}} Multiply the first fraction by the reciprocal of the second fraction.




{{{((u^3)(w^2))/((w)(uv^3))}}} Combine the fractions.



{{{(u^3w^2)/(uv^3w)}}} Multiply



{{{(u*u*u*w*w)/(u*v*v*v*w)}}} Expand. Remember, {{{u^3w^2=u*u*u*w*w}}} and {{{uv^3w=u*v*v*v*w}}}



{{{(highlight(u)*u*u*highlight(w)*w)/(highlight(u)*v*v*v*highlight(w))}}} Highlight the common terms.



{{{(cross(u)*u*u*cross(w)*w)/(cross(u)*v*v*v*cross(w))}}} Cancel out the common terms.



{{{(u*u*w)/(v*v*v)}}} Simplify.



{{{(u^2*w)/(v^3)}}} Regroup.



So {{{((u^3)/(w))/((uv^3)/(w^2))}}} simplifies to {{{(u^2*w)/(v^3)}}}.



In other words, {{{((u^3)/(w))/((uv^3)/(w^2))=(u^2*w)/(v^3)}}} where {{{u<>0}}},  {{{v<>0}}}, or  {{{w<>0}}}