First, group like terms and rewrite the expression as:
#((8 * 3)/(15 * 2))(a/a)((b * b)/b^4) =>#
#((8 * 3)/(15 * 2)) * 1 * ((b * b)/b^4) =>#
#((8 * 3)/(15 * 2))((b * b)/b^4) =>#
#((color(red)(cancel(color(black)(8)))4 * color(blue)(cancel(color(black)(3))))/(color(blue)(cancel(color(black)(15)))5 * color(red)(cancel(color(black)(2)))))((b * b)/b^4) =>#
#4/5((b * b)/b^4)#
Next, use these rules for exponents to multiply and simplify the #b# terms in the numerator:
#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#4/5((b * b)/b^4) => 4/5((b^color(red)(1) * b^color(blue)(1))/b^4) => 4/5(b^(color(red)(1)+color(blue)(1))/b^4) =>#
#4/5(b^2/b^4)#
Now, use this rule of exponents to complete the simplification of the #b# terms:
#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#
#4/5(b^color(red)(2)/b^color(blue)(4)) => 4/5(1/b^(color(blue)(4)-color(red)(2))) = 4/5(1/b^2) => 4/(5b^2)#
