#1#. Factor out #7# from the numerator and denominator.
#(14x^3y^6)/(7x^5y^2)#
#=(7(2x^3y^6))/(7(x^5y^2))#
#2#. Simplify.
#=(color(red)cancelcolor(black)7(2x^3y^6))/(color(red)cancelcolor(black)7(x^5y^2))#
#=(2x^3y^6)/(x^5y^2)#
#3#. Factor out #x^3# from the numerator and denominator. Recall the exponent quotient rule: #a^m-:a^n=a^(m-n)#.
#=(x^3(2y^6))/(x^3(x^2y^2))#
#4#. Simplify.
#=(color(red)cancelcolor(black)(x^3)(2y^6))/(color(red)cancelcolor(black)(x^3)(x^2y^2))#
#=(2y^6)/(x^2y^2)#
#5#. Factor out #y^2# from the numerator and denominator.
#=(y^2(2y^4))/(y^2(x^2))#
#6#. Simplify.
#=(color(red)cancelcolor(black)(y^2)(2y^4))/(color(red)cancelcolor(black)(y^2)(x^2))#
#7#. Rewrite the expression.
#=(2y^4)/(x^2)#
#:.#, the simplified expression is #(2y^4)/(x^2)#.
