First, we can rewrite this expression as:
#a = a^color(red)(1)#
#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#
#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#
#a^color(red)(1) = a#
#(12xy^3 - 9x^3y^7)/(3x^2y^5) =>#
#(12xy^3)/(3x^2y^5) - (9x^3y^7)/(3x^2y^5) =>#
#(4xy^3)/(x^2y^5) - (3x^3y^7)/(x^2y^5)#
We can now use these rules for exponents to simplify the two terms:
#(4x^color(red)(1)y^color(red)(3))/(x^color(blue)(2)y^color(blue)(5)) - (3x^color(red)(3)y^color(red)(7))/(x^color(blue)(2)y^color(blue)(5)) =>#
#4/(x^(color(blue)(2)-color(red)(1))y^(color(blue)(5)-color(red)(3))) - (3x^(color(red)(3)-color(blue)(2))y^(color(red)(7)-color(blue)(5)))/1 =>#
#4/(x^color(red)(1)y^2) - 3x^color(red)(1)y^2 =>#
#4/(xy^2) - 3xy^2#
