First, expand the terms with exponents outside the parenthesis using these rules of exponents:
#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#(2x^2)/((x^4)^3 * (2x^3)^2) = (2x^2)/((x^color(red)(4))^color(blue)(3) * (2^color(red)(1)x^color(red)(3))^color(blue)(2)) = (2x^2)/(x^(color(red)(4) xx color(blue)(3)) * 2^(color(red)(1) xx color(blue)(2))x^(color(red)(3) xx color(blue)(2))) =#
#(2x^2)/(x^12 * 2^2x^6) = (2x^2)/(x^12 * 4x^6)#
We can now use this rule for exponents to combine the #x# terms in the denominator:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#(2x^2)/(x^12 * 4x^6) = (2x^2)/(4 * x^color(red)(12) * x^color(blue)(6)) = (2x^2)/(4x^(color(red)(12) + color(blue)(6))) = (2x^2)/(4x^18) = (x^2)/(2x^18)#
We can now use this rule of exponents to simplify the #x# terms in the numerator and denominator:
#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#
#x^color(red)(2)/(2x^color(blue)(18)) = 1/(2x^(color(blue)(18)-color(red)(2))) = 1/(2x^16)#
