First, to make it easier to work with the individual variables rewrite the expression as:
#(a^3/a^-2)(b^-2/b^3)(c^4/c^2)(d/d^-3)#
Now, use these rules of exponents to simplify each term:
#a = a^color(red)(1)# and #x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))# and #x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#
#(a^color(red)(3)/a^color(blue)(-2))(b^color(red)(-2)/b^color(blue)(3))(c^color(red)(4)/c^color(blue)(2))(d^color(red)(1)/d^color(blue)(-3)) = #
#(a^(color(red)(3)-color(blue)(-2)))(1/b^(color(blue)(3)-color(red)(-2)))(c^(color(red)(4)-color(blue)(2)))(d^(color(red)(1)-color(blue)(-3))) = #
#(a^(color(red)(3)+color(blue)(2)))(1/b^(color(blue)(3)+color(red)(2)))(c^(color(red)(4)-color(blue)(2)))(d^(color(red)(1)+color(blue)(3))) = #
#(a^5)(1/b^5)(c^2)(d^4) = #
#(a^5c^2d^4)/b^5#
