Question 147996
{{{((8xy^5)/(5x^3y^2))((15y^2)/(16xy^3))}}} Start with the given expression.




{{{((2*2*2*x*y*y*y*y*y)/(5*x*x*x*y*y))((15y^2)/(16xy^3))}}} Expand {{{(8xy^5)/(5x^3y^2)}}}. Remember, {{{8xy^5=2*2*2*x*y*y*y*y*y}}} and {{{5x^3y^2=5*x*x*x*y*y}}}




{{{((2*2*2*x*y*y*y*y*y)/(5*x*x*x*y*y))((3*5*y*y)/(2*2*2*2*x*y*y*y))}}} Expand {{{(15y^2)/(16xy^3)}}}. Remember, {{{15y^2=3*5*y*y}}} and {{{16xy^3=2*2*2*2*x*y*y*y}}}



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



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



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



{{{((y*y)(3))/((x*x*x)(2))}}} Combine the fractions.



{{{(3y^2)/(2x^3)}}} Multiply.



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Answer:


So {{{((8xy^5)/(5x^3y^2))((15y^2)/(16xy^3))}}} simplifies to {{{(3*y^2)/(2*x^3)}}}.



In other words, {{{((8xy^5)/(5x^3y^2))((15y^2)/(16xy^3))=(3*y^2)/(2*x^3)}}} where {{{x<>0}}} or {{{y<>0}}}