First, rewrite this expression as:
#((2y)/(5b))/((4y^5)/(15by))#
Next, use this rule for dividing fractions to simplify the expression:
#(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)(2y)/color(blue)(5b))/(color(green)(4y^5)/color(purple)(15by)) = (color(red)(2y) xx color(purple)(15by))/(color(blue)(5b) xx color(green)(4y^5)) = (30by^2)/(20by^5)= (30color(red)(cancel(color(black)(b)))y^2)/(20color(red)(cancel(color(black)(b)))y^5) = ((10 xx 3)y^2)/((10 xx 2)y^5) =#
#((color(red)(cancel(color(black)(10))) xx 3)y^2)/((color(red)(cancel(color(black)(10))) xx 2)y^5) = (3y^2)/(2y^5)#
Now, we can use this rule of exponents to complete the division:
#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#
#(3y^color(red)(2))/(2y^color(blue)(5)) = 3/(2y^(color(blue)(5)-color(red)(2))) = 3/(2y^3)#
