First, simplify the division by using the rule for dividing fractions:
#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#
#(color(red)(5n^4)/color(blue)(p^3))/(color(green)(6n)/color(purple)(5p)) = (color(red)(5n^4) xx color(purple)(5p))/(color(blue)(p^3) xx color(green)(6n)) = (25n^4p)/(6np^3)#
We can now use these rules for exponents to further simplify this expression:
#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#
#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#
#a = a^color(red)(1)#
#(25n^color(red)(4)p^color(red)(1))/(6n^color(blue)(1)p^color(blue)(3))#
#(25n^(color(red)(4)-color(blue)(1)))/(6p^(color(blue)(3)-color(red)(1)))#
#(25n^3)/(6p^2)#
