Question 190785
{{{((4xy^2)/(-10x^2y^4))((15x^5y^3)/(12y^2))}}} Start with the given expression.



{{{((4xy^2)(15x^5y^3))/((-10x^2y^4)(12y^2))}}} Combine the fractions



{{{((4*15)(xy^2*x^5y^3))/((-10*12)(x^2y^4*y^2))}}} Rearrange the terms



{{{(60xy^2*x^5y^3)/(-120x^2y^4*y^2)}}} Multiply the coefficients



{{{-(xy^2*x^5y^3)/(2x^2y^4*y^2)}}} Reduce the coefficients



{{{-(x^(1+5)y^(2+3))/(2x^2y^(4+2))}}} Multiply the variable terms by adding the corresponding exponents



{{{-(x^6y^5)/(2x^2y^6)}}} Add



{{{-(x^(6-2)y^(5-6))/(2)}}} Divide the variable terms by subtracting the corresponding exponents



{{{-(x^4y^(-1))/(2)}}} Subtract



{{{-(x^4)/(2y^1)}}} Rewrite {{{y^(-1)}}} as {{{1/y^1}}}



{{{-(x^4)/(2y)}}} Simplify



So {{{((4xy^2)/(-10x^2y^4))((15x^5y^3)/(12y^2))=-(x^4)/(2y)}}} where {{{x<>0}}} or {{{y<>0}}}